The England international has reportedly agreed a deal to join New York City and could follow in David Villa's footsteps by joining the Australian club on loan beforehand
Spain forward Villa will play 10 matches for the Manchester City-owned Australian club before arriving at MLS outfit New York City, another brother club of the Premier League champions.
And Lampard, who announced in June he would be leaving Stamford Bridge after a 13-year stay, looks poised to follow Villa's path, having reportedly agreed a deal to join the MLS club in May, with former Chelsea team-mate Mark Schwarzer revealing the 36-year-old has taken an interest in the Australian city.
"All I can say is that he did ask me about Melbourne Heart [Melbourne City's former name]. He did ask me what Melbourne was like and what Melbourne Heart was like," former Australia international Schwarzer said, as reported by the Mirror.
"I said Sydney was the best place to live. But I spoke very highly of Melbourne. I actually love Melbourne. It's a great city. I told him how passionate in particular the Victorians are with their sport.
"There is huge potential in the game in Australia and it would be unbelievable if he went to Australia. I said to him that he would love living there. It's a great place to live.
"He walked away with that and I know what he's like. So we will see."