They claim the former AC Milan veteran, who has been linked with a move back to Serie A, is expected to open talks with a number of MLS clubs, if his contract isn't renewed at the Emirates.
Flamini has proved a useful squad member for Arsene Wenger since his return to the club in the summer of 2013. He has been in line for harsh criticism this season though, with his positional sense and awareness questioned on a regular basis.
Since Francis Coquelin established himself as the Gunner's first choice holding midfielder, Flamini has seen his first-team duties diminish, with only 16 Premier League appearances to his name this term.
Arsenal have Jack Wilshere, Aaron Ramsey and Santi Cazorla all yet to return from injury, and with the January purchase of Mohamed Elneny from Swiss side Basel, there seems to be little room for the Frenchman in the squad.
At 32, Flamini will still feel he has a lot to offer, and maybe a move to America would re-ignite his stalling career.