The Portuguese manager remains a popular figure at Stamford Bridge after winning two Premier League titles, two League Cups, an FA Cup and a Community Shield in his previous spell as Blues boss.
Gullit, who managed Chelsea between 1996 and 1998, is confident that he will return for a second spell with the West London club.
"I had a feeling already before the [Champions League] final that Mourinho was maybe coming to Chelsea," The Independent quotes Gullit as saying.
"From the moment Chelsea won it I think Mourinho said no because it's not a coincidence that he signed his contract just after, and therefore my instinct says he will be appointed.
"Chelsea want him for next season. That is my feeling, if it's right I don't know. I have no proof of that and I said it already before the final."
Mourinho managed Chelsea between 2004 and 2007.