The Sun says the Ghana ace, 25, has been telling pals he sees his future in London.
And with fellow countrymen Sulley Muntari and John Mensah no longer with the Black Cats, Gyan is even keener to move on. Bruce, though, is desperate to keep him because of his chronic lack of strikers and now faces a real dilemma if he wants to nab Crouch.
The move for Liverpool's David Ngog is on the rocks, so Crouch remains Bruce's No 1 target.
Yet Spurs boss Harry Redknapp will not let him go without something in return.
He said: "Crouchie is not one we want to sell if we can help it. Henderson has gone to Liverpool, so Sunderland have some money to spend. Perhaps Niall Quinn or Brucie will be on the phone trying to buy one or two of ours."