The Hammers have reportedly made a £5million bid for the Ghana captain and Appiah insists he wants to play for Alan Curbishley's side in the Premier League.
The 26-year-old hit out at Fenerbahce's claims he wants to stay in Turkey and has refused to go on the club's pre-season tour of Austria in a bid to force their hand over a switch to Upton Park.
He told The Sun: "I am very angry about stories saying I want to stay at Fenerbahce indefinitely.
"West Ham have expressed strong interest in me and I think Fenerbahce will have to listen to their offer.
"It is my ambition to play in the Premier League.
"At the start of last season I turned down offers from top clubs in Europe to help them lift the title because of my love for the team and fans.
"Even while injured I continued to play so they should also take my interest into consideration and listen to West Ham."