You probably "push" putts to the right. If you look at a putter face that actually aims dead straight at the intended target, but it "seems" to aim to the right, that is most emphatically NOT a vision or "optics" issue as so often claimed by dumb optometrists. What makes it "seem" aiming to the outside when in fact you KNOW it is not is the body's habit of sending putts offline to the right all the time. Then, when you look down at the putter face, wherever it is actually aimed, your BODY (not your eyes) tells your brain, "This putt is going to the right of where those guys say the putter face is aimed."
So the first order of business is to putt the ball ONLY down the line wherever the putter face gets aimed by anyone, no exceptions. Then the old "off to the right of the putter face aim" habit will start to die, and the "wherever the putter face aims is where this ball is going to start" stroke will come online as your new habit. Then the body won't fight your putter face aim; the actual aim of the putter face and what your body is getting ready to do for starting the putt off will agree.
I suggest scratching a little straight line on the green perhaps 6-8" long as the "stem" of a capital-letter T, and then draw / scratch the "top" of the T perpendicular to this. Place a ball about 1/4" down the stem from the intersection of top and stem, square the putter face up to the top of the T, and then challenge yourself to get the bottom of the ball rolled EXACTLY off the last grass blade at the bottom end of the stem, or die trying. It's a "yes or no" deal -- you either get this accomplished or you miss the last grass blade left or right. Later, on the course, you look at the putter face wherever it has been aimed as the top of this T, and then you identify the end of the imaginary "stem" perpendicular off the face of the putter 4-5" past the front of the ball, and then you commit to getting the bottom of the ball rolled over that spot (with good pace for distance), or die trying.
Later still, when aiming the putter face at a target some distance away for the start line, stand behind the ball and ""connect the dots" of ball and target with one edge of your putter shaft (held in front of your face sort of like a sword, viewing the edge with only one eye to eliminate a doubled image of the shaft). Once this "visual ruler" connects the dots, the grass blades along the full length of the shaft edge from ball to target are the REAL blades that make a single-file straight line. Good, now identify one about 4-8" in front of the ball to serve as the end of the stem of the T. Then square the putter face up thru the ball aimed straight at that end of the stem and send the ball off straight.
This gets the stroke fixed first, which corrects the bad body sense of where the stroke will go, and then next fixes the ability to aim dead straight at a distant target.
The business about the gaze is only something that supplements the above when "checking" the already-aimed putter face from beside the ball, to make yourself "happy" to simply putt where the putter face has been aimed, and is not really necessary if you are good at finding the end of the aiming stem from behind the ball. The objective is to KNOW that all strokes go ONLY where the putter face aims, and then the success or failure of the putt depends upon the reading and aiming, but the stroke is just stupidly easy -- send the ball wherever the putter face aims with any technique you feel like using for that stroke, with appropriate pace for distance.
Another thing to do is to set up a putter face with the toe about 1/4th inch back from the baseboard along a wall, the face "square" / perpendicular to the wall. Then putt a ball straight sideways along the baseboard, the ball not curling towards or away from the wall any but running a straight-sideways line that keeps the ball the same distance off the wall it started from at address (about 3" usually). Once you get this going, start trying to use the gaze to run your eyebeam like a laser with the dot on the carpet running a straight-sideways line along the baseboard, the same path the straight-rolled ball will travel. That skill requires a perpendicular gaze out of the skull and an apple-on-a-spinning-stick head-face rotation looking down the line with fixed gaze. This beside-the-ball skill will help you eliminate second-guesses and doubt about what sort of stroke is required and also help you stop missing the strokes off the line the putter face aims, and eventually will make you a better aimer whose strokes are always easy as pie to do well, once you decide the read and aim the putter according to what the read requires, given your delivery pace. Once the read and aim are decided and the putter face is sitting there aimed, that's it: no worries -- last thought how far for touch, and then pull the trigger and roll the ball down the start line defined by the aim of the putter face, any old way you feel like it.
Once aimed, no great putter has any question about HOW to putt, and simply sends the ball down the line where the face has been aimed. The OBJECTIVE of the stroke is what requires accomplishing. The objective is mandatory, and the technique HOW it gets done is merely optional. Accomplish the objective with every stroke, however you get it done, as that is the priority -- not technique. Within perhaps 2-3 weeks of this, you will LIKE not having to worry about the stroke, and will simply look at the putter face, see the start line, and then challenge yourself to make sure the bottom of the ball rolls off the end of the aiming stem with accuracy (and good pace).
On a practice, green, don't allow confusion about reading and aim start line. Find a modest 10-15 foot uphill putt with a little left or right break and figure out exactly what the read is for your delivery pace, so you know what target beside the hole to aim at, and mark it with another ball or tee peg. Then practice aiming straight at this target for the start line, from behind the ball finding the end spot of the "stem", and then positioning the putter face behind the ball aimed dead at the end of the starting "stem" flushed up to the top of the T. Then watch to make sure your stroke goes exactly where the putter face got aimed -- exactly over the grass blade at the end of the "stem" -- no exceptions, ever, for any reason, no kidding. The success or failure of the putt cannot be allowed to depend on you "coming up" with some stroke that "fixes" any lingering problems in the read or the aim. Once aimed, that's it. Send the ball down that line or quit golf and take up bowling.
If these putts don't go in the hole, then either your aiming is off or the read is wrong. If you recheck the aiming and it is correct, then the problem is your reading is not good.
If you reach this point in golf, that's a great thing, because now all the confusion about what is the real problem is cleared out of the way. That's the great benefit of always putting ONLY wherever the putter face has been aimed, no exceptions: you FIND OUT where you aimed for probably the first time ever, and this allows you to find out whether you are any good at reading putts, and THAT allows you to get better at reading and aiming putts. here are 27 or 36 (or even more) other benefits as well, but I won't bother enumerating them presently.
Putting Coach and Theorist