The 36-year-old is a free agent after Chelsea decided against offering him a new deal at the end of last season.
New York City are owned by Manchester City owner Sheikh Mohammed Mansour, with Australia side Melbourne City and Japanese outfit Yokohama F Marinos also part of the City Football Group stable of clubs.
With New York City not starting their debut season in MLS until March 2015, it is understood that Lampard could play for Melbourne City in the A-League on a short-term deal.
New York City have already signed Spain's all-time leading goalscorer David Villa from Atletico Madrid, with the 32-year-old loaned out to Melbourne for three months before the start of the MLS season.
Lampard spent 13 seasons at Chelsea and became the club’s all-time record scorer with 211 goals, winning three Premier League titles, the Champions League, the Europa League and four FA Cups during his time at Stamford Bridge.
He has won 106 England caps and was part of the 23-man squad for the World Cup, captaining the national side in the 0-0 draw with Costa Rica.
Glad to see the new york daily news is ensuring lampard gets the welcome he deserves. thinking mans footballer? pah- bobsy