Italian striker David Di Michele, on a season long loan deal with West Ham from Torino, had been linked with a return to Serie A.
However, Di Michele, who has scored twice in six starts for the club, has no plans to turn his back on the Premier League in January.
He said: "I am at West Ham. I hope to do well, to return to play and to score as many as possible.
"Then it's down to the two clubs to speak about my loan deal.
"My limited playing time is perhaps due to the fact that I have a player like Bellamy, who is not just anybody, ahead of me.
"Or maybe that having started strongly I have also been affected by the team's drop in form in a difficult tournament."