Lampard is a free agent after announcing last month that he would be leaving Chelsea at the end of his contract after 13 years at Stamford Bridge.
Both Lampard and Villa are set to move to the MLS next March to play for New York City, and the duo are expected to feature together at Manchester City's A-League franchise in Melbourne prior to the Big Apple switch.
Former Australia and Chelsea goalkeeper Mark Schwarzer has fuelled speculation that 36-year-old Lampard could move to Melbourne City after revealing his ex-Chelsea team-mate had asked him about life in the Victoria state capital.
"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,” Schwarzer told The World Game.
"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."