Contractor Multiplex has always insisted the troubled stadium development, designed by HOK Sport with Foster and Partners, will come in on time, despite spiralling costs.
However, there are fears that disputes between Multiplex and the landowner, Quintain Estates, have thrown the construction of a main walkway - and the overall project - behind schedule.
The £757 million Wembley development was due to be completed by 31 March this year, allowing the new stadium to be handed over to the Football Association in time for the cup final on 13 May.
But, according to one national newspaper, the parties are at odds as to whether delays starting work on a key pedestrian access, a construction phase which is expected to last 20 weeks, will push the project over the agreed deadlines.
A Multiplex spokesman said: 'We planned to begin construction of the 'pedway' in September, but Wembley National Stadium and Quintain only resolved their difficulties in time for us to start work on that site today.
'We've had meetings over how we can accelerate what is a 20-week job, but there's only so much we can do over a problem that was nothing to do with us. It's causing us major concern.'
Quintain, meanwhile, appears to be less worried. A representative said: 'All issues have been resolved to ensure Multiplex has sufficient time to complete the works before March 31.'
It is understood Multiplex has already lost almost £75 million on the development and, if the stadium cannot open in time, this year's FA Cup final could again be played in Cardiff.