"If he breaks my records, then that means good things," the NY legend tells TMZ Sports.
Tiki holds a grip of Giants records ... but it's his 1,860-yard, single-season rushing total that many have said could be within reach for Barkley by season's end.
And, if you think Barber is secretly hoping the star rookie falls short of that ... you'd be wrong.
"That means good things for the New York Giants," Tiki says.
Barber's ex-teammate, Amani Toomer, seems to think it's certainly possible the record falls this year ... 'cause the ex-receiver tells us Saquon was undoubtedly the most impressive NFL rookie of Week 1!!