The Italian international is currently the subject of a two-week suspension, imposed on him by the club after he allegedly headbutted teammate Jose Fonte in training.
There is a strong chance that record-signing Osvaldo, who Juventus are interested in, could depart St Mary’s before tomorrow’s 11pm deadline, although Pochettino refused to give much away when quizzed about the subject this afternoon.
He said: “At the moment there is no news regarding Dani Osvaldo.
“There is still a day and half left to finish the transfer window activity so there’s many things that can happen in that time.
“Anything is possible.”
Pochettino had revealed on Monday that Saints are looking at possibly signing one player before the window shuts.
However, he says it is not simple to find the right player at this time of year.
“Signing right now someone who fits the profile we are looking for is not easy,” he said.
“It’s very complicated to find that player.”