Signed in the summer from Roma, there have been continued reports linking Osvaldo with a swift return to Serie A.
He has recently been absent from Mauricio Pochettino's side after collecting a three-match ban and a £40,000 fine for his part in a touchline bust-up in the 1-1 Barclays Premier League draw at Newcastle last month.
His latest misdemeanour, however, could mean there is no way back for Osvaldo after the club released a statement on Thursday morning.
"Southampton Football Club has today suspended striker Dani Osvaldo for two weeks, following an incident at the club's Staplewood training ground," it read.
"The club has taken swift and proper action for what it considers a breach of the conduct expected of its players.
"Southampton will be making no further comment at this time."
The club-record signing, who played under Mauricio Pochettino at Espanyol, was also fined and suspended at former club Roma for punching team-mate Erik Lamela during a 2-0 defeat to Udinese.
He will now miss Saturday's FA Cup fourth-round tie with Yeovil as well as Premier League fixtures against Arsenal and Fulham.
Since signing for Saints in the summer Osvaldo has scored three league goals, including a memorable equaliser in the 1-1 draw with Manchester City on December 7, with injury and suspension limiting the former Fiorentina and Bologna man to just 14 first-team appearances to date.
The training-ground incident is the latest story in a week which has seen Southampton make plenty of headlines.
Nicola Cortese resigned as chief executive last week, sparking rumours about the futures of manager Pochettino and a number of their high-profile players.
Saints' owner Katharina Liebherr has moved to steady the ship and, with Pochettino insisting he will remain in charge of the team, things had appeared to calm down before Osvaldo's scuffle.
Osvaldo may be missing from the FA Cup tie with Yeovil this weekend but Saints' assistant manager Jesus Perez is looking forward to seeing some of the club's younger players take centre stage against their Sky Bet Championship opponents.
"For us the glory is in trying to play nice football and to try and show our best quality in each game and try to make our supporters happy," he said.
"The FA Cup gives you the opportunity to get more success and it's important for us now to get ready for the next game, try to make it into the next round and also to give some minutes and opportunities to our younger players."
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- Mauricio Pochettino
- Southampton Football Club
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