Hull boss Steve Bruce says defender Paul McShane must apologise before he can resume training with the club's first-team squad.
The reason behind the rift has yet to be revealed by either Bruce or McShane.
"If he apologises to myself and the squad, he will come back into the fold. It's entirely up to Paul," Bruce said.
"Paul knows exactly why he's training with the Under-21s squad at the moment."
Republic of Ireland international McShane, Hull's longest-serving player, has retweeted comments from fans about his exile, but Bruce has urged him to explain the rationale behind it.
"I heard all this nonsense about what's on Twitter and the rest of it," added Bruce.
"He's been quite quick to reveal that he is in there and I hope he comes out and tells the reason why."