The Saints paid £12.8million for Italy international Osvaldo in August 2013 but he failed to settle at St Mary's and was suspended by the club for a training ground incident before joining Juventus on loan.
Despite an exodus of stars, including forwards Rickie Lambert and Adam Lallana, new Southampton manager Ronald Koeman is thought to be keen to offload Osvaldo, 28, and believes he can secure the services of Inter midfielder Taider in the process.
Taider, 22, was part of the Algeria side who made a favourable impression at this summer's World Cup 2014 - the unfancied African team taking eventual winners Germany to extra-time in the last 16.
With the big-money sales of Lallana, Luke Shaw and Calum Chambers, Koeman has plenty of funds available and Sky Sports understands the Dutchman is targeting no fewer than five new arrivals in addition to Taider in the coming weeks.
Celtic keeper Fraser Forster, Aston Villa's Ron Vlaar and Sporting Lisbon defender Marcus Rojo, along with the Norwich duo of Leroy Fer and Nathan Redmond, are all thought to be among Southampton's targets as they look to plug the holes left by their departures.