The Chelsea legend spent last season on loan at the Etihad from sister club New York City.
He officially returned to America at the start of the last MLS season but has struggled to settle due to a succession of calf and hamstring injuries.
Lampard has made just nine appearances, scoring three goals.
And Goal claim City have extended an open invitation to the 37-year-old so he can get back to full fitness.
GETTY
Frank Lampard could return to Manchester City to train
GETTY
Lampard spent last season on loan at City but is not expected to make a playing return
The legendary midfielder has made it clear he will not return to England to play but may well take the opportunity to come back and get fit before the MLS resumes in March.
“I need the rest to be fully fit next year for the club," he said.
“My aim now is to manage myself well for next season, to finish this season on a high, have some breaks at times, but keep ticking over, have a really good pre-season and throw everything into next year."
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