Midfielder Faye, 33, last played a competitive match for Stoke City in August 2009 and has been training with Leeds.
Faye, who could feature against Swansea City at Elland Road on Saturday, is expected to adopt a defensive midfield role.
Simon Grayson said: "I can't see him being a box-to-box player as he's always had a career as a central midfield player and a centre-half as well.
"But what he can do is put a foot in and tackle. He's a different type of player to what we have got at the club already."