"He won't return any phone calls," Browns general manager John Dorsey told Cleveland.com on Thursday.
Dorsey is planning on bringing a number of wide receivers in next week and said Bryant would be among that group if he would pick up the phone.
"Maybe he's still thinking about other stuff," said Dorsey.
Dorsey's comments drew an immediate response from Bryant, who posted on his Twitter account Thursday night: "I wouldn't mind playing for the Browns.. I just want to be right first."
A little while later, Bryant tweeted that he will begin visiting with teams and announced that he would indeed visit Dorsey and the Browns next week.
Starting my visits next week...I’m coming to the Land to see you Mr Dorsey— Dez Bryant (@DezBryant) August 10, 2018
The Browns could use some extra bodies at the position. Josh Gordon remains away from the team to work on his health and treatment plan, and Cleveland traded Corey Coleman to the Buffalo Bills on Sunday.
Rookie Antonio Callaway, who was elevated to a starting role following the trade of Coleman, could face potential disciplinary issues. He was cited for possession of marijuana during a traffic stop over the weekend.
Bryant was released by the Dallas Cowboys in a salary dispute after spending eight seasons with the franchise.
A three-time Pro Bowl selection, 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-worst 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 reel in 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 named a first-team All-Pro selection that year.