"I'm embarrassed to even tell you how many times I tried," Kosar, the popular former Browns quarterback, told USA TODAY Sports on Tuesday. "I have tried to call him directly 18 different ways. If he chooses not to talk to me, that's his choice.
"I'm not mad at him. But there's a point where there's an element of respect that's involved."
Kosar, 52, said he is concerned that Manziel's excessive partying could cut short the 23-year-old's career.
"That's definitely a possibility,'' said Kosar, who played for the Browns from 1985 to 1993 and is the team's second all-time leading passer. "I'm not saying he doesn't have a chance to change, but that's a possibility."
One of the first orders of business for the new Browns coach will be to decide whether he wants to keep Manziel. Earlier this season former head coach Mike Pettine demoted Manziel to third string for lying about partying during the bye week.
Manziel reportedly was in Las Vegas on the Saturday night before the Browns' final regular-season game despite being in the NFL's concussion protocol that sidelined him for the game against the Pittsburgh Steelers. He missed his mandatory concussion treatment on gameday at the team's facility.
Manziel was videotaped drinking, including on Christmas Eve, during the season. He spent 73 days in inpatient addiction-rehab center in the offseason.
"I can't comprehend him not wanting to be (at the game) because maybe he'll pick something up, maybe he'll get the intensity of it, maybe he'll learn a trick play, maybe he'll see what you're going to have to do hopefully next year and show your commitment to the team," Kosar said.
Manziel finished his second season with 1,500 passing yards, seven touchdowns and five interceptions in nine appearances (six starts) and a passer rating of 79.4. He rushed for 230 yards.