Javier Saviola is targeting a move to England after agreeing to part company with Olympiakos.
Fabio Borini’s agent has claimed the striker wants to stay and fight for his place at Liverpool.
The 32-year-old defender was the man who lifted the trophies in Mourinho's first spell as boss from June 2004 to September 2007 and has been skipper since, but he will receive no favouritism from the Portuguese.
"He's not safe, and he knows he's not safe," Mourinho said.
"The only thing he knows is safe is our friendship, our relationship, but professionally, nobody's safe.
"I need to be honest with everybody and I think he appreciates that. We spoke about it and he understands perfectly.
"We used to say in Portugal: friends are friends, but business is 'apart'. This is kind of a business.
"In football, you have to prove yourself every day and every week.
"I trust him completely. I know he's a very good player, but he has to prove himself like everybody else.
"I feel the motivation is there, the pleasure of training and playing is there.
"His class is there. His position is there. From a physical point of view, he needs to work hard and not have injuries because injuries break the evolution of the player.
"For me, that's the key point for John."
Mourinho is happy with his squad and has just one transfer target: Manchester United striker Wayne Rooney.
The pursuit of Rooney has led to question marks over the future of Fernando Torres, who has struggled at times since his January 2011 arrival at Stamford Bridge from Liverpool in a £50million deal.
Mourinho is confident of rejuvenating the World Cup-winning Spaniard.
"I think I know Fernando quite well in terms of a player," said Mourinho, who believes Torres is at his best when he can run in behind defences.
"I think I know the best way for a team to play to try to get the best out of him, so I will try to help him, the same way I try to help other people."
Torres is trying to rediscover his former self, but Mourinho is eager to experience further success at Chelsea, rather than rely on his reputation.
"I don't want to be loved for what I did before," he said.
"I want to be loved because of what I'm doing now and what I will do in the future."