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.
Mourinho won two Barclays Premier League titles, an FA Cup and two League Cups during his first spell at the club from 2004-07.
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."
With the two sides who finished above Chelsea in the Premier League - City and Manchester United - also changing their managers before next season, Ba thinks Mourinho's past experience at Stamford Bridge could give the club an advantage.
The 27-year-old said: "Definitely. He knows everything about Chelsea having already managed the team for three or four years. He knows everybody here and he knows the club.
"But all three clubs are looking for success and to win trophies.
"I think there is going to be more competition around the league."
Defender David Luiz also feels it would be exciting to work under Mourinho, who has also coached Porto and Inter Milan on the grandest European stage.
Luiz said: "Everyone says positive things about him and everyone knows about his qualities.
"He has done a great job in many clubs in the world, like Chelsea.
"We would be excited to work with an experienced coach like that."