Cole was kept out of the first team by Cesar Azpilicueta for much of last season, making just 17 Premier League appearances, his lowest total in a single campaign for the club.
He was in tears after the final home game of the season, and claimed last month that he is likely to leave Stamford Bridge, tweeting: "I am weighing up my options for playing next season with my agent and sadly it does not look like chelsea (sic) will be one of them."
Veteran defender John Terry has penned a one-year contract extension but England midfielder Frank Lampard has brought the curtain down on his glittering career in west London after a 13-year association with the club.
Mourinho insists Cole, who has attracted interest from all over the world, is in a 'different situation' to Lampard, and says he plans to hold talks with the former England left-back before his contract expires on June 30.
The Chelsea manager, talking at a pre-World Cup event for Yahoo for whom he is working for in Brazil, said: "With Frank Lampard I spoke a couple of weeks before the end of the Premier League, with Ashley I didn't get that chance.
"They are different situations. I want to see what is going on, what is going to happen. But I will speak to him."
Mourinho, meanwhile, believes Lampard will return to the club in some capacity in the future.
He claims Chelsea owner Roman Abramovich has made it clear he wants Lampard to return to the west London outfit as soon as his playing career is over.
And Mourinho admitted it was difficult having the face-to-face meeting with Lampard to discuss their parting of ways.
"You can't imagine how difficult it was," he said. "But at the same time, I can feel some happiness about the process because, for sure, he comes back to Chelsea.
"Mr Abramovich - the No.1, the most important person - wants very much for Frank to be back, I want him to be back, the staff want him to be back, so he comes back, for sure.
"The other thing is that he can come back the way he wants. Mr Abramovich has left the door completely open for him on the understanding Frank can do anything he wants at this club.
"He can come back when he wants and, to repeat Mr Abramovich's words, the way he wants.
"He can be a coach, he can start at the academy, he can start being my assistant at the same time because he is doing his coaching badges or he can start in a different role.
"He can decide: 'I don't want to start immediately at the coaching role, I want to be an ambassador, I want to work hand in hand with the CEO, representing the club in important places of our life.'
"It's not the end of Frank Lampard's career in Chelsea. It's just a little break.
"He is one of the most important players in the history of the club."