What would make it non-conforming? I have a couple similar to this and love them.

I only been told so by some stranger, that’s why I wonder. Is it the grip? Shaft? Head? Or is it just the guy who thinks so...

Have one myself don't think is non-conforming

May be something with the grip, however, looks conforming to me- perhaps you could check with a local pro

I tend to side with Chris, I'm no expert though. It has all the markings of Titleist and seems conforming. I have an old bullseye with flange. Maybe you were making too many putts and taking the guys money(?).

I once met a guy on the putting green who had a putter head made of wood with couple of metal bars for weight. He thought the world of it, he bought it off some woodcrafter whose name was branded on it. Now that I think would not be conforming unless the the guy sent it in for approval.

Even long putters are conforming when not anchored. At least on the Champions Tour there are still a couple of Bull’s Eyes still in use.

It should be conforming. Bullseye style putter have been around for a long time and the grip looks like a standard grip. You could always look on the USGA website or email them if you are concerned. They make and keep the conforming club list. Nice of an "expert" to say it is non conforming without the basis for their opinion.

Scotty did a marvellous job with his version of the BullsEye. A true homage to the original!
If your club is nonconforming, I'd guess it might be the grip, but, after spending a bit of time on the USGA site and rereading the equipment section, personally I think whoever told you that is probably just jealous of what is truly a classic and desirable club. I'd check with your club pro, but, I think you're just fine.
I have a '60's BullsEye I still use on occasion, and it's a marvelous club. Elegantly simple. Johnny Miller won the 1973 U.S. Open at Oakmont with one, breaking the course record by finishing with an 8 under par 63. Yep, great putter!
Let us know what you find out, and good luck.

Doubtful your putter doesn't conform but would suggest as per the rules below that you check that the grip's flat front extends to within 1 inch of the top and bottom of the grip.

ii) Putters
As clearly stated in the Rule, a putter grip may have a non circular cross-section, provided that, amongst other things, the cross-section remains generally similar throughout the length of the grip.

In order to accommodate the popular (and somewhat traditional) “pistol-type” putter grips and also limit the amount of potential offset, the phrase “generally similar” is interpreted to mean: (i) that the butt (top) end of the grip must not involve a sharp change in slope or dramatic flare on the underside (ii) that the flat front must extend to within 1 inch (25.4 mm) of the top and bottom ends and (iii) if the axis of the grip and the shaft do not coincide, the grip must be at least 10 inches (254 mm) in length

Thanks for all respond, Have myself play professional golf for 7 years and Did qualify for The Open Championship 2016 so for me that a stranger told me that the putter is non-conforming is strange.. Have heard from the person i question that it not ok to putt from two sides. Or have a putter that is two sideways and can be putted from left and right side.. What can I say.. Golf is not always easy.
Kind Regards
Adam