Koeman last month revealed that the Premier League club were looking to sell the Italy striker after he failed to report for pre-season training.
Osvaldo was loaned to Juventus in January for the remainder of last season and could be heading back to Serie A as Inter strive to take him to San Siro, with midfielder Taider potentially heading in the other direction.
Koeman told BBC Radio Solent: "We are looking for the best for Osvaldo and the best for the club.
"Taider brings quality and we need that. We need competition in the squad as well and that will be good."
The Dutchman stated that Southampton are closing in on three new signings after losing Rickie Lambert, Luke Shaw, Adam Lallana, Dejan Lovren and Calum Chambers.
"We hope to do that this weekend and then we have two weeks still to prepare for the Liverpool game," said the former Netherlands defender.
Algeria international Taider, who played in the recent World Cup in Brazil, joined Inter from Bologna in a co-ownership deal last year and made 25 Serie A appearances in his first season.