The Championship side are preparing for their first season back at the highest level.
Aitor Karanka is keen on signing the 32-year-old as he looks to add depth to his ranks following their automatic promotion from the Championship.
Though the former AC Milan man has struggled for opportunities at the Emirates this season - he has made just 16 appearances in the top flight - his experience would surely help Boro as they look to re-establish themselves at the highest level.
The partnership that Adam Clayton and Grant Leadbitter have formed at the Riverside Stadium has arguably been one of the most impressive in the second tier. However, the latter of the pair has not played in the Premier League for around seven years while Clayton - who began his career at Manchester City - has yet to play in the top flight.
Having Flamini's knowledge around the squad will help the side adapt their style having spent the previous couple of seasons perfecting their game to get out of the Championship.