West Ham could face FA Cup expulsion if Fifa finds the club breached rules over the selection of striker Diafra Sakho.
Fifa rules state a player cannot appear for his club if he is meant to be on international duty.
World football's governing body has begun an inquiry but the Hammers "vigorously" deny any wrongdoing.
If West Ham are found guilty, Fifa could order the Football Association to overturn their victory over the League One side.
Fifa is investigating a "potential violation" of its regulations by both the club and striker Diafra Sakho over his selection - but has declined to give a timescale on proceedings.
The Hammers are set to visit Premier League rivals West Brom in the FA Cup fifth round on Saturday, 14 February.
The Football Association is refusing to comment but is believed to be aware of Fifa's investigation.
Senegal are angry Sakho featured for West Ham, albeit as a substitute, 48 hours before they were knocked out of the Cup of Nations.
The Hammers insist the player had a back injury that prevented him from flying and claim he was driven to Ashton Gate in a limousine for the FA Cup tie on 25 January.
A Hammers statement claimed Fifa's inquiry was "clearly unfounded" and requested its dismissal.
West Ham boss Sam Allardyce said he was advised not to select Sakho for Saturday's 2-0 loss at Liverpool while the dispute was ongoing.
And unless the matter is resolved this week, Sakho looks set to miss Sunday's home game with Manchester United.
Bristol City declined to comment on reports they would seek £250,000 in compensation if Fifa finds West Ham broke the rules.