The France international has largely been used as a substitute and is now into the final year of his contract.
The report goes onto state that Galatasaray representative Cenk Ergun will fly to London next week to hold talks with Arsenal.
Galatasaray already have strong links with the North London club following the transfer of Lukas Podolski this season.
Flamini provided two assists and scored on goal in 33 appearances for Arsenal last season.
The Lions are on the lookout for a new defensive midfielder following reports Felipe Melo could be on his way of Istanbul.
Galatasaray won the league title for a record 20th time last season and booked a place in next seasons Champions League group stages.