The veteran Englishman has confirmed his decision to join New York's latest franchise, but is not expected to make a short-term stay in Australia as part of the deal
The 36-year-old has agreed a two-year deal with New York City, who are set to make their Major League Soccer debut in 2015.
Spanish striker Villa will also be a part of New York City's inaugural squad, but will time at Melbourne City ahead of the new season kicking off in the United States next year.
It was widely expected Lampard would follow suit in a bid to retain match fitness after ending his glittering stay at Chelsea.
However, the experienced midfielder does appear likely to join John van 't Schip's new-look, rebranded A-League outfit.
"There are no plans in place for Frank to come to Melbourne," a club spokesman was quoted as saying by the Herald Sun.