Lampard has agreed to join New York City ahead of their first campaign in MLS next year, but a decision is yet to be made on how the veteran will keep fit ahead of the 2015 season in North America.
Fellow high-profile recruit David Villa will spend time at Melbourne City, who are also bankrolled by Premier League champions Manchester City, before linking up with their sister club in the United States.
A similar arrangement had been mooted for Lampard, only for reports to suggest the former Chelsea man will not be following the Spanish striker to Australia.
A loan move to England's top flight for the first half of the season could also be a possibility, with New York City's director of football Claudio Reyna poised to reveal the club's decision.
"We're discussing what's going to happen with Frank," Reyna told reporters.
"It's been a key topic for us this week and I think we'll have an announcement soon. We need a good solution for us, selfishly for NYCFC, to make sure he's playing at a good level."
