The duo missed yesterday's 2-1 win over Bournemouth and Ronald Koeman says it's possible neither player will feature until after the upcoming international break.
Keane suffered a gash to his foot that will rule him out of Thursday's Europa League clash with the Cypriots while Jagielka has a minor hamstring complaint.
"It's not so bad," Koeman said of Keane's injury yesterday. "His foot was a little bit open and the doctor said he will maybe reach next Sunday but he will be doubtful for Thursday.
"I think he cannot start on Thursday but maybe yes on Sunday.
"Jagielka has a slight hamstring problem and will be one week to 10 days out and we will not take that risk before the international break.
"We did not have seven normally starting players today so it is even more of a compliment to the players who played today for what they showed."