The financial uncertainty at Upton Park has led to speculation that Hammers boss Gianfranco Zola may be forced into selling his best players.
Zola outlined his determination to keep his leading figures earlier this week and admitted he would be 'very annoyed' if he did lose any members of his squad.
Bellamy has also spoken of his happiness at West Ham recently after he was linked with a return to Celtic where he previously spent a spell on loan.
However, he admitted he was unsure if the Hammers would accept any bids, and Sky Sports News understands that Spurs are now trying to test their London rivals' resolve.
Negotiations between the two clubs are understood to have started, with West Ham keen to recoup almost double the £7.5million they paid for Bellamy 18 months ago.