The Senegalese international was the speculation of intense media interest during the January transfer window, mainly due to the £3.5million release clause written into his Hammers contract, after he arrived at Upton Park from Wigan Athletic on a Bosman free last summer.
West Ham owners David Sullivan and David Gold have been eager to tie Diame to a new-and-improved deal - omitting the current clause - but contract talks are believed to have broken down, due to his excessive salary request.
That leaves the door open for suitors Arsenal and Spurs to activate his release clause in the summer, with both Arsene Wenger and Andre Villas-Boas attracted by the cut-price deal to sign Diame.
No bids were lodged by either of the north London rivals on deadline day, but the 25-year-old might have to pick between White Hart Lane and the Emirates Stadium at the end of the season, if talks with West Ham remain in deadlock.
Opening talks between player and club already ended acrimoniously when West Ham told Diame his demands would not be met, and Tottenham and Arsenal will continue to monitor the situation with intent over the coming months.