James Webster's side are due to face Championship rivals York City Knights in the showpiece event on Saturday.
However, they have notified the RFL that the Covid outbreak has "raised concerns about their ability to participate" in final.
An RFL statement read: "A squad of players who have tested negative are taking additional precautions since testing to ensure that they minimise any further risk of contracting the virus.
"To recognise the risk of further transmission and in line with the Multiple Case Framework, the RFL’s Multiple Cases Group have determined that an additional round of PCR tests for the Featherstone squad should be conducted on Thursday evening.
"The results will be received overnight, allowing a decision on the viability of the match on Friday morning.
"Featherstone and York are determined to make every effort to fulfil the match, with thousands of their supporters relishing the prospect of a Wembley appearance."
Ironically, despite plenty of Covid outbreaks in Super League, causing numerous games to be postponed or cancelled in recent weeks, second-tier clubs have hardly been affected by the pandemic in 2021.
The RFL has waived the requirement of the teams to name 21-man squads today, 48 hours in advance of the match, because of these unusual circumstances.
It says it has also agreed with the clubs to make this announcement so that supporters are aware of the situation.
If the match is postponed, Featherstone and York supporters will be entitled to apply to have their tickets refunded, if they no longer wish to attend Wembley on Saturday. Full details of how to claim a refund will be confirmed on Friday should it be necessary because of the game not going ahead.