Recent media reports have suggested the Portuguese will leave Real Madrid at the end of the season and go back to Stamford Bridge, a prospect that Chelsea vice-captain Lampard is clearly relishing.
"I think it would be a great thing for the club. I think he is a fantastic manager," Lampard told British newspapers.
"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."
Mourinho led Chelsea to two Premier League triumphs in his previous spell at Stamford Bridge from 2004-07 before moving on to Inter Milan and then Real.
Lampard's contract with the European champions expires at the end of the season.
Asked if he would like to stay if Mourinho took over from interim manager Rafael Benitez, the 34-year-old midfielder replied: "Yes I would but let's see what happens.
"I've always said I want to spend the rest of my career here. I think everyone knows that."
Lampard, one goal away from equalling Bobby Tambling's club record total of 202, is set to feature in third-placed Chelsea's Premier League fixture at Aston Villa on Saturday.
