He left Stamford Bridge as the club's record goalscorer with 211 from 648 appearances during a 13-year spell in west London.
It is understood Lampard was impressed by the Manchester City and New York Yankee-owned club's vision.
Should Lampard sign, the midfielder may follow the lead of another recent recruit, Spanish record goalscorer David Villa, in joining their sister club, Australian-side Melbourne City, to maintain fitness ahead of the MLS season in March 2015.
(Reporting By Tom Hayward; editing by Amlan Chakraborty)
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