Bryant, accompanied by his agent, Kim Miale, huddled with Cleveland team officials for two days before departing late Friday morning.
Cleveland.com, citing a source, reported that Browns general manager John Dorsey and Miale will continue their discussions.
A three-time Pro Bowl selection, Bryant has been without a team since the Dallas Cowboys released him in mid-April in a salary dispute.
Bryant sat down with Cleveland's in-house broadcasting team and spoke favorably of the city, adding that he thought he would look good in the orange uniform of the Browns -- the same color he wore at Oklahoma State.
"I'm happy to be here, you know excited, you know just trying to work out some things," Bryant said. "It's a lovely place."
"That would be awesome," Taylor told Cleveland.com last week. "I've said this before. We know what type of talent Dez brings to the football field. He's been a very, very good player in his time throughout this league and he adds talent to the wide receiver room.
"I hope it can get done, but like I said that's up to management. I definitely think he could help this team."
The Browns have some uncertainly at wide receiver. Josh Gordon remains away from camp because of health issues and rookie Antonio Callaway could be subject to disciplinary action by the league after he was cited for possession of marijuana.
Bryant had a team-leading 69 receptions for 838 yards and six touchdowns with Dallas in 2017. The 29-year-old has gone a career-long 23 regular-season games without a 100-yard performance.
Since signing a five-year, $70 million contract in 2015, Bryant has failed to record a 1,000-yard season or make more than eight touchdown receptions in a season.
Bryant was a touchdown machine in the first half of his career with the Cowboys, hauling in 41 scoring passes in a three-season span, capped by a career-high 16 in 2014. He was selected first-team All-Pro that year.