Sport Mediaset say the Uruguayan playmaker wants to remain in European football despite various media outlets suggesting he wants to return to his homeland to play for Penarol.
Ramirez, 24, was once Saints' record signing but current boss Ronald Koeman has not shown any desire to play the midfielder during his tenure at the South Coast club.
Last season Ramirez was loaned out to Premier League relegation fodder Hull City and he has not been close to featuring for Southampton in the 2015-16 season so far - despite a glaring absence of creativity in the Saints midfield.
Bologna, who Southampton signed Ramirez from for £12million, are supposedly interested in Ramirez - as well as Rome giants Lazio.
There were strong rumours surrounding the future of Ramirez, suggesting Saints were willing to terminate his contract to allow him to move on.