The Italian international has been given a two-week suspension and is thought to have been placed on the transfer list, which many of his Southampton team-mates believe is the outcome he wanted from the Staplewood spat.
Reports claim Jose Fonte was the recipient of Osvaldo's actions with boss Mauricio Pochettino now believed to have lost patience with the club's record signing from Roma and is ready to sanction his sale.
But Southampton may only be able to recoup £10million of their £15million outlay on the 28-year-old striker who was also fined and suspended by his former club after allegedly punching Erik Lamela in 2011.
Osvaldo was already serving a suspension for his part in a touchline altercation in December's draw against Newcastle and would have missed this weekend's FA Cup fourth-round clash against Yeovil Town.
He will now additionally miss the Premier League games against Arsenal next Tuesday and the trip to Fulham on February 1.
Inter Milan are leading the race to sign Osvaldo before the end of the January transfer window as they need a striker in quickly and Saints may be able to push them to nearer £12million if they play their cards right.