The Spain international has refused to return to the London from his exile in Brazil since the summer, and according to the recent reports, the Blues have cleared out his locker room and have moved his car to the youth team car park.
When asked about the rift between Costa and Blues manager Antonio Conte, Allardyce told talkSPORT: “Well, I would never text players to tell them that, I would call them into my office and tell them face-to-face.
“With Costa, it doesn’t look like it’s reparable now.
“When he’s told to train with the youth team, that’s Antonio Conte wielding his power as a manager. Antonio is brave to do that, because it would be very difficult now for him to call Diego Costa back and ask him to play for Chelsea again.
“If I’m going to take that stance with a player, I make sure that I’m definitely not going to bring them back, and I definitely won’t have to rely on them at one stage or another.
“For me, the strange thing is that he seemed to overcome his problems and had a good season last year with Conte.
“He had a major contribution to Chelsea winning the Premier League and seemed to be enjoying his football. Then, all of a sudden, I don’t know if it was the China thing or not, at the end of the season there’s this rift about wanting to go back to Spain and then not turning up.
“It was different to Coutinho at Liverpool, for example. That was obviously Barcelona who came in and started that problem, whereas there didn’t seem to be any real big bids from anybody to take Costa, a fantastic centre-forward who scores goals, away from Chelsea.”