Chelsea manager Roberto Di Matteo said that those outside the club "will have to wait and see" if John Terry remains as Blues captain.
Terry was banned for four matches and fined £220,000 after an independent Football Association regulatory commission found him guilty of racially abusing QPR defender Anton Ferdinand.
After announcing that he would not be appealing against the decision and issuing an apology for his actions on Thursday, Terry's suspension begins with Saturday's Premier League visit to London rivals Tottenham Hotspur.
Chelsea released a statement saying they had launched internal disciplinary action against the 31-year-old, but that any measures taken would remain confidential.
Speaking ahead of the Spurs game, Chelsea manager Roberto Di Matteo said: "We do not discuss publicly the disciplinary matters we take against our players. They remain confidential. You will have to wait and see. They are internal matters, the action we take against our players, and we are not going to discuss it."
Terry was handed the captain's armband at Stamford Bridge at the start of the 2004-05 season, and has since led the Blues to three Premier League titles, four FA Cup triumphs and the Champions League, although he was suspended for the final against Bayern Munich.
He was also named England captain in 2006 but was stripped of the honour on two occasions, firstly in 2010 for tabloid revelations over an extra-marital affair and again earlier this year with regard to the Ferdinand case, which led to Terry announcing his retirement from international football.
Asked whether it was suitable for Terry to remain captain, Di Matteo said: "Over the many years he has been here he has shown a lot of qualities. He has realised that on that day he fell below his standards and the clubs standards.
"For that he has received a ban and a fine and more action from the club. He is being punished for what he has said. We have all made mistakes in our life before.
"We appreciate he has not appealed the ban and the fine and that he has apologised publicly for the language that he used. He has apologised generally to everyone, including the Ferdinand family.
"It wasn't a matter of not apologising directly. It was a matter of apologising to everyone for the language used in that game. He knows it was not appropriate and he has been banned and fined for that."