The midfielder recently became the club's all-time leading goalscorer, and says he hopes the manager can restore the doggedness of his past regime if he decides to come back.
The England international believes Mourinho would make the team more dogged as they bid to compete against the two Manchester teams, who will also be sporting new managers next year.
"If Jose comes back it will be a huge lift for the club," Lampard told the Daily Mirror. "It's no secret that he's an idol for the fans for what he's done. He's the greatest manager in our history and he changed the whole belief of the club and made us into a winning club. It will lift the fans, and I know it will lift the players."
He added, "When we won under Jose before we got criticized for the fact that we were so dogged - but we must certainly get back to being a bit more dogged.
"It doesn't mean taking away the beautiful football because when you have the players we have, three No.10 types who are so versatile, then you have to cater for that and get them into your team to win games."
Lampard believes the departure of Sir Alex from Manchester United could signal a slight weakening of the Premier League champions, and pinpointed a title challenge as Chelsea's key aim next term.
"I think the changes at United and City give us more chance, although they've raised the bar," he continued. "It's going to be a huge change for them and whether they can adapt remains to be seen."
"There's a little bit of relief that Sir Alex has gone because I have huge respect for him and watching him on the touchline with his aggressive manner and passion. It's a huge priority to be challenging for the league again next season. And I would love to win the Premier League again, for sure."