John Sivebaek, Gravesen's agent, last night confirmed the midfielder has no intention of joining Sheffield United and will stay and fight for his place.
"It is hard to imagine Thomas in Sheffield," said Sivebaek. "At this moment he has decided he will stay. He has gone back for training and is now using all his energy to fight his way back into the team.
"It is his intention to stay with the Scottish champions and show everybody is wrong about him.
"He likes to live in Scotland and likes the club and the fans. The problem is playing time on the pitch. Now he has given himself time to fight his way back in and I think he is able to do that. Celtic have given no indication they will not accept that."