"Cedric will not be ready for Sunday, and Shane Long has got an issue in his calf. So we've got some players with a problem today," Pellegrino told a news conference on Friday.
"Maybe tomorrow we'll review, and we'll decide how he (Long) is. The doctor will check, but today he couldn't train, it is a little bit sore in the calf. Tomorrow we'll make a decision.
"Most of my players are ready to compete and with the fixture calendar we have in the next two months, that is good news for us."
Southampton, who have lost three of their last four league matches, dropped to 11th in the standings following their defeat at the Etihad Stadium and have seven league games left this year, including clashes against Arsenal and Chelsea.
Pellegrino expects another tough test at Bournemouth, who have been trying to establish themselves in the top flight under manager Eddie Howe since gaining promotion in 2015.
"Obviously I know that Bournemouth is a side that wants to grow and wants to be little by little getting better every year," he said.
"They try to keep the base of the team and most of the team grew together, and every year they try to be stronger even at home because in the last few games they have been picking up points.
"I think it will be really tough."
Sunday's south coast derby match will be only the fifth Premier League encounter between the two sides, with Southampton winning 3-1 at the Vitality Stadium last season.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
