The 34-year-old midfielder won two Premier League titles and three other major trophies during Mourinho's three-year spell at Stamford Bridge.
"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.''