The Uruguayan international has been told he is free to leave St Mary's.
The Uruguayan international has failed to make an impact at Southampton since joining the club in an eye-catching move back in 2012.
He is now reported to have three main suitors for his signature, according to Tutto Mercato Web.
They claim that a meeting is underway today between Boro and the player's representatives over a potential move for the player - either on loan or permanently. With his contract expiring in the summer it is likely any deal would eventually become permanent.
Meanwhile Swansea City are also said to be keen. New Swans boss Francesco Guidolin is keen on the player, who he knows from his time playing in Serie A.
Swansea are therefore prepared to offer him a move from the South Coast and, for the time being, Premier League football.
His former club Bologna are also said to be keen but they are considered outsiders in the running.
Ramirez has featured just five times for Southampton this season and has not scored for the club since December 2013.