Jeffries said: "The words 'Wembley' and 'fiasco' seem to have been appearing in every sentence of newspaper reports – the real fiasco is in the accuracy of the reporting."
He added that the coverage had changed the public perception of the scheme, but denied that it had hindered progress towards finalising contracts.
He said that he was looking forward to signing the contract this week, after which he would be free to explain fully the real situation.
"I am 99% confident that the deal will be signed this week, but we do have some minor problems to iron out before final completion."
The plans for the stadium were also due to be unveiled this week by Football Association chief executive Adam Crozier, culture secretary Tessa Jowell and Sport England chairman Trevor Brooking.
It is understood that the £420m loan agreement between the Football Association subsidiary Wembley National Stadium Limited and German bank WestLB is close to being sealed.
Demolition and enabling works on the site will begin as soon as the final contracts have been signed. A source close to the deal said contractor Multiplex will be appointed on a 39-to-40-month building contract.
‘Fiasco’ seems to have been in every sentence of newspaper reports
Work will have to begin immediately for the stadium to be completed by the 2006 FA cup final.
The source said: "There is a provision for financial incentives for the contractor Multiplex to complete the project on time, and it is hoped that these economic benefits will help the project to run smoothly."
The source added that plans were being drawn up for half-capacity events after completion to test the facilities.
It is understood that the construction costs remain around the £410m mark, as was first revealed in Building in May.
The stadium has been designed by the World Stadium team, a joint venture between original architect Foster and Partners and HOK Sport.