The in-form Austrian has been linked with moves to Manchester United and Chelsea during recent weeks.
The interest in the signature of Arnautovic grew recently after the player’s brother and agent Daniel suggested that he now needs to be playing European football.
Arnautovic has managed to reinvent himself as a player since he moved from being a winger to a forward.
The 29-year-old has been one of the best players for the Hammers this season so far as he has managed to notch five goals from 11 League games.
The East Londoners have been in poor form this season and are only three points above the relegation zone following their 4-0 thrashing against Manchester City last weekend.
It is essential that they retain the services of Arnautovic in January if they want to maximize their chances of having a successful season.