Wembley Stadium Ltd and the Football Association have each refused to confirm whether the building of the new stadium is suffering further delays.
Wembley was originally meant to host the FA Cup final on 13 May
Wembley, which will not be ready for May's FA Cup final, is scheduled to host the Community Shield on 13 August.
But BBC Sport understands that rugby league's Challenge Cup final on 26 August could have to be held elsewhere, casting doubt on the Community Shield.
"We have contingency plans in place," an RFL spokesman told BBC Sport.
"We have a contract with Wembley, but we have not yet been told that there is a problem or that we won't be able to hold the game there."
Speculation in Thursday's newspapers suggested the final of British rugby league's main cup competition could be moved to Twickenham, the HQ of rugby union in England.
An RFU spokeswoman confirmed the stadium was available on 26 August, but refused to comment on whether the organisation had been in talks with the RFL.
"There has been a lot of speculation and we don't want to add to that at the moment," said the spokeswoman.
About 35,000 Challenge Cup final tickets have been sold, with many fans travelling to London from rugby league's heartland in the north of England - meaning another venue in the capital is the most likely destination if Wembley is not ready in time.
The BBC has also learned that the delay has also affected four music concerts scheduled for this year.
The building of the stadium has suffered numerous problems, with a roof beam collapsing last week, resulting in building work being cancelled for a day.
There have also been problems with underground sewer pipes at the stadium and workers were sent home on Tuesday after disputes over pay and threats of redundancy.
"We're working with Wembley and Multiplex and we want to get the stadium open at the earliest possible date," an Football Association spokesman told BBC Sport.
But the speculation has also cast doubt over England's Euro 2008 qualifiers in September - which are meant to be the first time the national football team will play at the redeveloped ground.
The official deadline for the handover of the stadium will be passed on Friday with the FA still waiting to hear exactly when the builders will finish the stadium.
Multiplex are due to make an announcement to the Australian stock exchange on what progress they have made.