Jim Brown wants Cleveland to take a RUNNING BACK with the 1st overall pick in the NFL Draft ... and he's crossing his fingers for Saquon Barkley.
The Hall of Famer was out in D.C. on Tuesday -- just days before he flies out to Texas to announce the 2nd round pick for his former team.
So, with the 1st round kicking off on Thursday night ... we had to ask for Brown's wish list.
"I think Mr. Barkley would be a wonderful addition to the Cleveland Browns," Brown tells TMZ Sports ... "I would hope that they pick him number one."
Brown says he doesn't have any inside information on Cleveland's draft plans -- but adds, "I really like him."
As for the unsolvable puzzle in Cleveland ... quarterback ... Jim says there are 4 solid guys, but he doesn't have a clear-cut favorite.
Stay tuned ...