Accommodation at Number 10, a Grade I listed building, has been stretched to breaking point. But moving would provoke accusations that Mr Blair was empire-building, creating a prime minister's department to override Whitehall.
A second option would be for his office to expand into nearby government buildings such as the Foreign Office or the Cabinet Office. In the short term, this is regarded as a more likely prospect by his advisers.
The plans emerge in a book, The Powers Behind The Prime Minister: The Hidden Influence of Number Ten, by the academics Dennis Kavanagh and Anthony Seldon, published by HarperCollins this month. After the Prime Minister recruited extra staff in 1997, they say, the physical layout at Downing Street was "impacting adversely on working practices".
An executive secretary and board of management was set up, which considered the expansion into neighbouring government offices. "Another idea, welcomed by a number of staff, has been the suggestion that they move out of Number 10 completely," the book says.
A Downing Street spokes-man said last night: "A new building has been vaguely talked about, but there are no plans and it is not a serious proposition. Number 10 is a very historic building and that is what it will remain."