Papy Djilobodji has returned to the Academy of Light but Charlie Methven says that the club are considering their legal options.
The defender did not report for pre-season training after a loan move to Dijon FCO last season, but failed to secure a transfer in the closing stages of the summer window.
Sunderland withheld his wages in that period.
Some markets remain open but with options dwindling, the 29-year-old has returned to Wearside.
Sunderland are considering legal options with the impasse likely to continue.
Methven said: "The club is considering its legal options.
“The two cases aren’t identical in that finally Papy Djilobodji has turned up, but nonetheless turning up in the first week of September rather than at the beginning of August in a fit condition to play, as was agreed.
“There is an internal procedure going on to determine whether he is fit to play.”
Black Cats boss Jack Ross said the matter would now stay in the hands of the club's ownership.
"Papy is back," Ross said.
"Beyond that, because of how the situation has developed and how it will probably continue to develop, it goes beyond me.
"I can't really comment on it other than to say that Stewart [Donald] and Charlie [Methven] have stressed that they'll be the only ones who comment on where his future lies and how it will develop for the club.
"We've said it often enough, a solution would have been best a long time ago and that still remains the case."
Djilobodji has not joined team-mates in training, having not played since last season and not had any pre-season programme to speak of.
His fitness is therefore well short of other players at the club.
While Ross cannot say whether he expects the Senegalese man to return to the fold, he admitted earlier this week that he believed it unlikely.
"I can't really comment on the situation," Ross said.
"But the one thing we've obviously tried hard to do is build a spirit quickly within the group and the players have done that really well. I think that they appreciate that and want to maintain it.
"We're conscious of that and that's how we've approached every player we've brought to the club."
Didier Ndong remains AWOL with the club unaware of his whereabouts.
He is also not receiving his wage after failing to report for pre-season.
The Gabon midfielder had a number of opportunities to leave the club this summer, with Torino, Leganes and Benfica all making moves for his services.