Lute Olson: Luke Walton Proved Himself ... Will Be Great NBA Coach

Luke Walton just got a LEGENDARY co-sign from one of the biggest names in basketball coaching history ... who says Walton has already proved he's got what it takes to be a head coach in the NBA.

TMZ Sports spoke with Luke's college coach Lute Olson -- who's in the Basketball Hall of Fame after a historical run at the University of Arizona.

Olson tells us he's been paying very close attention to how Walton's doing as the interim coach of the Golden State Warriors -- and says he's convinced Luke is ready for a full-time role.

"Just watching him on the sideline, he handles himself really well. He is a great communicator. I can tell the players really like him and respect him."

Walton is currently filling in for Steve Kerr -- who also played for Lute -- and Olson says he couldn't be more proud of his proteges.

As for Luke, Olson believes it's only a matter of time before he gets a serious job offer from another team.