EXCLUSIVE

Saquon Barkley was rockin' a NY Giants sweatshirt to a Pennsylvania barber shop and TMZ Sports has the photos.

Of course, there's a lot of buzz that the former Penn State running back is being targeted by the Giants -- who have the #2 overall pick in the NFL Draft.

Is it a good sign for NY Giants fans? Sure ... but don't go celebrating just yet.

Sources close to Barkley tell us the sweatshirt was a gift given to him from the Giants when he met with the team -- and it just happened to be laying around when he needed a shirt to go get a haircut.

FYI -- we're told players are often given team swag during pre-draft visits.

In other words ... Barkley's position is that he'd still be happy to be drafted by any team.