The Hammers and the Premier League have also rejected a request by the Argentina striker's representatives to have his registration cancelled.
Tevez's camp want to try to re-start his transfer to Manchester United by doing the same deal that took Javier Mascherano to Liverpool.
In order to do so, the Hammers would have to agree to cancel his registration but it is understood both the club and the Premier League have refused to do so.
A letter from Tevez demanding for his contract with West Ham to be terminated was received on Tuesday and has been rejected, as has a separate letter to the club and the League from his representatives about his registration.
It is now becoming increasing likely that FIFA will have to step in to break the stalemate.
West Ham pointed to last Friday's statement by chairman Eggert Magnusson, which stated: "Carlos Tevez is a registered West Ham player, contracted to the club until June 2010. There is no agreement with West Ham for Carlos Tevez to leave the club."
West Ham realise that if they do anything contrary to the Premier League's instructions they could be left open to further disciplinary action over third-party agreements.
FIFA say they may be prepared to step in to settle the transfer dispute - but they have yet to receive any official request to do so.
Football's world governing body can become involved if there is an international element to a transfer or if they are asked by the Football Association.
The Argentina striker's representatives are preparing to call on FIFA and the FA after his proposed move to Manchester United stalled due to the Premier League's insistence that West Ham must receive the bulk of the reported £30million fee.
Tevez's representative, businessman Kia Joorabchian, says he owns the player's economic rights.
A FIFA spokesman said: "We have not received any official request from any of the parties involved so far.
"If we do receive a request we would then decide whether we have to look at it or if it is up to the FA to rule on it.
"The FA could also ask us for guidance and send us all the relevant information."
Manchester United have agreed terms with Tevez and Joorabchian and hoped to have everything tied up last week - but the deal has now reached an impasse.
It is understood Tevez's camp believe the Premier League can no longer act as independent arbiter in the case.