The Daily Star Sunday says Noble has just one season left on his current deal and is eager to sign a long-term extension to the club he has served for his entire career.
Hammers are delaying any more talks until the season is well under way as they put the pressure on one of their stars.
A club insider said: "The signing of Mohamed Diame from Wigan is going to increase the competition in midfield. Let's see how Noble reacts to that. That will be pivotal in whether he gets a new deal or not."