The Hammers key man is currently out injured with a hamstring tear but could be fit to return at some point next month.
Diame signed on a free transfer from Wigan in the summer and has a £3.5million buy out clause in his contract but the East End club have recently offered the all action playmaker a new deal dismissing that problem.
West Ham are yet to win a game since Diame pulled up in their defeat to Liverpool, including a humiliating loss at Reading yesterday.
QPR are desperate to add more talent to their struggling side as they sit bottom of the Premier League going into the New Year.
Arsenal, Newcastle and Stoke City have all been linked with a move for Diame in January so the big spending Rangers will have their work cut out to nab his signature.