There have been reports that the Serie A leaders are close to announcing the loan signing of Osvaldo.
The 28-year-old, who is currently suspended by the Premier League club following a training ground bust-up with Jose Fonte, is said to be close to joining the Bianconeri until the end of the season with a view to a permanent deal.
But Pochettino would not be drawn when quizzed on the issue at a press conference on Thursday.
"At the moment there is no news regarding Dani Osvaldo," the Argentine said.
Asked if it would be possible for Osvaldo to play for Saints again after the incident, Pochettino said: "Your question answers itself, if you know what I mean, meaning no. It's clear."
On the situation, he continued: "We have to wait [to see whether he goes].
"There is still a day and half left and he is suspended at the moment and we shouldn't get ahead of ourselves.
"As soon as anything happens about this matter the club will make it public.
"It's clear this is something that no one expects. It's completely unpredictable and something we did not expect. In light of that there is no explanation I can give."
But when asked what the chances are out of 10 of Osvaldo going to Juventus, he said: "I don't know because I'm not in charge of that situation. Anything is possible."
Then when asked if he could sign for Valencia, Inter Milan or West Ham, he added: "All is possible."
Osvaldo signed for the Saints in the summer from Roma for £15million but has failed to make an impact under Pochettino.
He has scored four goals in 16 appearances for the south coast club.