Osvaldo joined the defending Serie A champions on loan from Southampton with a view to a permanent move on Friday after falling out of favour with the Premier League club.
However, the Italy international will not feature against Inter, with rumours suggesting that the former Roma man has been omitted as his fitness levels do not meet coach Antonio Conte's expectations.
The 28-year-old has not played since Southampton's 1-1 draw at Newcastle United last month, when he was involved a touchline melee that resulted in him receiving a three-match ban.
Osvaldo was then suspended for two weeks by Southampton earlier this month for a "breach of the conduct expected of its players" after allegedly headbutting team-mate Jose Fonte at a training session.
As a result, the former Fiorentina man has not played since that trip to St James' Park on December 14.
Southampton signed Osvaldo from Roma in a deal worth £15million in August, however the Buenos Aires-born player has since scored just three goals in 13 appearances for Mauricio Pochettino's men.
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