The Portuguese is widely expected to leave Real Madrid and return to Stamford Bridge to take over from Rafael Benitez in the summer.
Mourinho led Chelsea to Premier League titles in his first two seasons in charge, but he walked out on the club in September 2007 following reports of a bust-up with owner Roman Abramovich.
But he is a firm favourite to be offered a second spell at Chelsea, and goalkeeper Cech said: "With Jose Mourinho we had great success in the past and people still have great memories and admiration for him.
"If he comes back, the story will be interesting for everyone. He will be more than welcome."
Cech also paid tribute to Rafael Benitez, who was given a torrid reception from Chelsea fans after he was appointed as interim manager following the sacking of Roberto Di Matteo.
"It was not easy for him, with the reception he got," Cech added. "But he came here to help and to improve the situation for us and to do as best as possible. That is what we did, what he did, what the coaching staff did.
"This is maybe the reason why it's worked so far and we're in the Europa League final."