The midfielder brought to an end his 13-year stay at the club on Monday, and leaves Chelsea as their all-time top scorer, having won a plethora of trophies.
Mourinho's strong relationship with Lampard has been well publicised, and the Portuguese waxed lyrical over his former player, insisting the door at Stamford Bridge will always be open for a return.
"You can't imagine how difficult it was for him to leave," he said.
"I think only he knows because we spoke - not by phone, in person - but at the same time I can feel some happiness about the process because for sure he comes back to Chelsea one day. For sure.
"Everybody wants it, Mr (owner Roman) Abramovich - the number one, the most important person - wants very much Frank to be back, I want him to be back, the staff want him back, so he comes back for sure.
"And 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 try things, feel where he is better suited, we can feel as a club where he can give us more, but 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 in this moment whether he wants to start immediately in a coaching role, or if he wants to be an ambassador, representing the club in important places of our life - he can do what he wants."
