However, his only start of the 2009/10 season came in the win over Leyton Orient in round two of the Carling Cup.
Meanwhile, former Liverpool midfielder Salif Diao, who is also out of contract at the Britannia Stadium, is in talks about taking a dual role at the club.
Diao, also 33, has been with Stoke since October 2006 and made 81 appearances for the club.
Amdy was an important member of the squad during his two years here, especially during our first campaign in the Premier League
Stoke boss Tony Pulis
Manager Tony Pulis told the club website: "Salif is fantastic to have around the place and he is an important character to have in the dressing room.
"He also has some very good contacts and it would be beneficial for us if we could work closely with him to hopefully uncover a few potential stars of the future."
On the departure of Faye, Pulis added: "Amdy was an important member of the squad during his two years here, especially during our first campaign in the Premier League."
Academy graduate Nathaniel Wedderburn has also been told he can leave the Britannia Stadium, having failed to make a first-team appearance.
Source: BBC Sport
Source: BBC Sport