No deal was expected Thursday night, a source told ESPN's Adam Schefter. The two sides will continue talking and "will know more tomorrow."
Bryant said on Cleveland Browns Daily radio show that he likes the city, thinks he would look good back in the orange he wore at Oklahoma State and said "we are just trying to work some things out."
He retweeted a photo of himself signing autographs in Cleveland's airport. Several Browns have been lobbying Bryant, including quarterbacks Tyrod Taylor and Baker Mayfield, and receiver Jarvis Landry.
Bryant, 29, was released by the Cowboys after eight seasons in April. The three-time Pro Bowler was the franchise leader in touchdown receptions.
He turned down a three-year contract offer from Baltimore, preferring a one-year deal where he can re-establish himself and get a bigger payday next season.
"I tell everybody that shows up here, we don't care by what means you get here," Browns offensive coordinator Todd Haley said Wednesday. "If you're willing to put your hand in the pile and work and be part of moving forward and having success, I am all for it."
On Tuesday, Browns coach Hue Jackson said the team would do its "homework" before meeting with Bryant.
"It's a very open and candid conversation with guys about how your locker room is, how your team is run, how we go about doing things and see if it fits," Jackson said. "The player has to be honest and we have to be honest with what our expectations are and just lay it out."