The Saints have enjoyed a good recent record against the Swans, losing just three of their 10 Premier League encounters, including a 1-0 win in this fixture last term - when Charlie Austin scored the only goal.
Southampton, who have never won a home game on the opening weekend of a Premier League season, will still be without Virgil van Dijk as he continues to train away from the rest of the first-team squad, having handed in a transfer request.
Pellegrino is expected to hand debuts to summer signings Mario Lemina and Jan Bednarek, as Saints go into the new campaign seeking a top-eight finish for a fifth consecutive season.
Having kept Swansea up last term, Paul Clement has endured a tough summer on the transfer front and looks set to lose Everton target Gylfi Sigurdsson - who will not be involved on Saturday.
Clement is also without injured trio Ki Sung-yueng, Nathan Dyer and Fernando Llorente, but new additions Roque Mesa and on-loan striker Tammy Abraham could make their debuts.