The fiery Italy international was already sitting out a three-match ban for his part in a touchline brawl against Newcastle, which he got involved in despite being on the bench at the time.
He was then suspended for two weeks by the club for breach of conduct,” as he attacked team-mate Fonte during a game between ranks on Wednesday and left the defender with a black eye.
There are rumours Osvaldo actually head-butted Fonte during the training ground incident and drew blood from his nose, which may well have brought his six-month spell at Southampton to an abrupt end.
Osvaldo was also dropped from Italy’s Confederations Cup squad in May for publicly hurling abuse at then-Roma coach Aurelio Andreazzoli after the Coppa Italia Final.
Italian media claim Osvaldo has no particular intention of staying with Saints, while the Daily Mail suggest he was “unpopular and arrogant” within the squad.
Inter are hoping to take advantage of the tense situation to grab Osvaldo on loan, as Southampton will now be eager to remove the tempestuous striker from their squad.
Juventus had also been interested in the past, but would be less likely to want someone with such a poor disciplinary record now.
Fiorentina are an intriguing option, as Coach Vincenzo Montella already worked with Osvaldo at Roma and they need a forward after injuries to Mario Gomez and Giuseppe Rossi.