The flamboyant Portuguese boss is expected to take charge at Stamford Bridge for a second time this summer after it was confirmed he is to leave Real Madrid at the end of the Spanish season.
Blues goalkeeper Petr Cech, who arrived in the same summer as Mourinho nine years ago, said: "He is a great manager and I think everyone remembers how successful we were with him as a manager. If he could reproduce that it would be fantastic."
Chelsea have been under the caretaker charge of interim boss Rafael Benitez - one of Mourinho's great rivals - since Champions League winner Roberto di Matteo was sacked last November.
Benitez overcame huge fan hostility born out of his past associations with Liverpool to steer the club to Europa League glory and a place in the Champions League once again.
The Benitez reign comes to an end after Chelsea take on Manchester City in the second of two lucrative post-season friendlies at Yankee Stadium in New York this weekend.
Real Madrid conclude their campaign on June 1 and a new appointment is anticipated soon after that.
Striker Demba Ba, who only joined the club in January, is also positive about the prospect of being managed by Mourinho.
The Senegal international said: "We will see if he joins us first - but you see what he has won, what he has brought to his teams and to his players individually, and of course he is one of the best.
"Everybody is thinking about it and everybody is happy. They know that he is a person that wants to win."
- Sports & Recreation
- Rafael Benitez
- Real Madrid