The Sunday Mirror says Huth will snub bids to take him back to Germany to go on fighting for his first team place at Stoke.
Bundesliga club Hamburg tried to sign the Berlin-born defender in the summer.
A friend said: "I would ask one question - if you were a player at Stoke in the Premier League, why would you want to go to either Hamburg or Cologne?
"Robert loves the game in England.
"And Stoke can offer him far more in football terms than any of those clubs in Germany."