The 30-year-old Irish defender, who arrived at the Stadium of Light from Manchester United this summer, is struggling with a hamstring strain picked up on his Black Cats debut in their friendly against Arminia Bielefeld.
Asked whether O'Shea would be fit for the game at Anfield, manager Steve Bruce told the club's website: "We don't think so, and it would be unwise of me rush him back.
"He's close, but he's got a hamstring strain so we have to make sure he's right.
"When he is right and plays he'll be all the better for it because John O'Shea is a big acquisition for this football club."
He will also miss Ireland's international friendly against Croatia at the Aviva Stadium on Wednesday night.