Sources told NFL Network that Brown has not made an official request for a trade.
Brown, 30, pulled in 104 catches for 1,297 yards and a league-high 15 touchdowns in 2018. He did not play in the Steelers' final game of the season due to a reported benching. The benching followed a series of missed practices and a reported disagreement with Roethlisberger.
Roethlisberger said in a 93.7 The Fan radio interview on Tuesday that Brown has not been responding to his calls and text messages. Brown is under contract through 2021 and is set to make more than $15 million next season.
He sparked additional trade rumors on Tuesday by responding to a message from San Francisco 49ers tight end George Kittle, who asked him "what's up?"
The four-time All-Pro responded to the message with a star-eyed smiling emoji.
Brown fueled even more trade rumors to the 49ers by liking a photo of himself on Instagram which showed him wearing a 49ers jersey.