The 34-year-old midfielder won two Premier League titles and three cups during Mourinho's three-year spell at Stamford Bridge.
Current Real Madrid coach Mourinho is favourite to replace Chelsea's interim boss Rafael Benitez.
"I think it would be a great thing for the club, I think he is a fantastic manager," Lampard said.
"I've seen speculation before and a completely different manager walks through the door so we never know on that front but he is certainly one of the greatest managers, if not the greatest, in world football, so I'm sure the club and the fans will be happy to have him.''
Lampard, whose Chelsea contract expires at the end of the season, was asked if he would like to stay if Mourinho got the job. ''Yes I would, but let's see what happens," he replied. "I've always said I want to spend all my career here. I think everyone knows that.''
Interim boss Benitez will leave the club at the end of the season and Mourinho, who is expected to exit Real Madrid at the same time, has been widely tipped to return to the club where he was manager between 2004 and 2007.
Earlier this month the Portuguese fuelled the speculation by saying: "I know in England I am loved. I know I am loved by some clubs, especially one".
His agent, Jorge Mendes, told Italy's Radio Mana Mana last week there is an "80%" chance the Portuguese will return to Chelsea in the summer.
Source: DSG
Source: DSG