The 29-year-old Frenchman is available on a free transfer, and the former-Arsenal player has been linked with a number of Premier League clubs, including West Ham and Fulham.
His wages have proved to be a stumbling block though, with Flamini reportedly holding out for £75,000-a-week.
The former-AC Milan star left the Italian giants this summer after his contract was allowed to run down, and he's been training with Arsenal to stay in shape.
The report claims Arsene Wenger may firm up his interest with the offer of a contract if he fails to land Cabaye.
There is a feeling that Cabaye favours an Arsenal move over Paris St Germain, but the Gunners are refusing to match Newcastle's £20m-£25m valuation of the midfielder. Arsenal reportedly do not want to go above £15m.
Flamini is a back-up alternative for Wenger though, as the Arsenal boss looks to strengthen his defensive midfield options.
The France international spent four years at Arsenal, making more than 100 Premier League appearances for the north London club.