Allardyce has options at the back of course, with Steven Taylor is pushing for a place and Charles N'Zogbia happy to drop back to left-back.
But has settled on Faye, Claudio Cacapa, Habib Beye and Jose Enrique in recent weeks.
All four were summer signings with Enrique, a £6.5m acquisition from Villarreal, the most costly.
Enrique, 21, needed time to adapt physically to the English game but Allardyce is confident he has the real thing on his hands.
Allardyce: "We want to see him get forward more and more, but his defending side is better than I thought it was.
"As a young man I hope I am eventually going to have a complete left-back there who is going to be a bit of a force in the Premier League."