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After initial delays, work on the new stadium was set to be finished in time for soccer's Community Shield on August 13.
But that game, along with an England soccer friendly in August and two Euro 2008 qualifiers in September and October, will now be played at other venues.
The completion delay means that rugby league's Challenge Cup final on 26 August will also be held elsewhere.
The official deadline for the handover of the stadium was due to take place on Friday, but the FA is 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.
Wembley was originally supposed to stage the FA Cup final on 13 May as well as the Football League play-offs, but the decision was made to move them to Cardiff in February.
Meanwhile, it has been reported that the Challenge Cup final will be moved to Twickenham, the HQ of rugby union in England.
"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."
An RFU spokeswoman confirmed the Twickenham 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.