Noble, 27, has made 18 total appearances for the Hammers this season, but the impending arrival of Darren Fletcher could make him expendable at Upton Park.
The Manchester United man is said to have been offered the chance of regular first-team football in order to beat off rival chasers West Bromwich Albion and Valencia and, with Alex Song and Cheikhou Kouyate well-established in the line-up, Noble is set to be the odd-man out.
The Baggies themselves would also be interested in a move for the Irons vice-captain with their Fletcher pursuit set to come up short, although potential bidders would need to improve upon his £40,000-per-week wages to lure him from his childhood club.
He is coming to the end of his current West Ham deal, but has an option for a further two seasons in the summer which, if triggered, would see his wage package rise to £50,000-a-week.
The former England Under-21 international has made 305 total appearances for the club since his 2004 debut but, despite his fan favourite status, could be allowed to move on with Morgan Amalfitano and Kevin Nolan providing enough midfield cover.
With both QPR and West Brom facing a potential relegation battle over the second half of the season, Noble’s leadership and experience would be a huge asset to either dressing room, although it remains to be seen what kind of fee his services would command.