The £757million project is over budget and behind schedule, with the FA Cup final due to be hosted at the new stadium on May 13, 2006.
Since 2001 the FA Cup final has been played at Cardiff's Millennium Stadium in Wales, and the venue has been booked to host next year's final as a precaution.
"If (builders) Multiplex are true to their word and true to their ambition we have every chance of staging the Cup final at Wembley," Barwick said. "If not we will do it at the Millennium Stadium. I will be at the 2006 FA Cup final but I don't know what stadium I'll be at. I hope it is Wembley."
Multiplex is scheduled to hand over the stadium to the FA for test events in March.
