Clark will have a scan on a foot problem on Monday, while Peralta is suspended as Rangers return to action at Ibrox after three successive away victories.
Defender Bilel Mohsni is available again after serving his one-match ban following his sending off after the final whistle in the 1-0 win at Airdrie.
Midfielder Lewis Macleod also has a chance of returning after missing Sunday's 2-0 win at Stenhousemuir due to a calf strain.
Defender Steven Smith and midfielder David Templeton are still absent along with longer-term casualties Chris Hegarty and Ross Perry.
East Fife striker Nathan Austin hopes to be fit to face Rangers after going over on his ankle in the 1-0 win over Arbroath last weekend.
Greg Paterson will continue in goal for the Fifers after Michael Andrews departed the club and signed for Berwick Rangers.
East Fife have already lost 5-0 at Ibrox this season in their league clash in August as well as going down 4-0 at home to the runaway leaders in October.