The Department for Culture, Media and Sport has discussed with Falconer the possibility of appointing a government minister to keep a closer eye on the quality of design in public sector buildings.
The appointment would be someone close to the Treasury, to increase its influence across government.
The current chief secretary to the Treasury, Paul Boateng, has been mentioned as a candidate.
It’s gone a bit quiet and keeping momentum of the ministerial group is very difficult
One Whitehall source said that the current system made it hard to get all the design champions in one place.
The source said: "It's gone a bit quiet and keeping the momentum of the ministerial group is very difficult."
The process is on hold until after Tony Blair's summer reshuffle of government ministers, which could bring in new faces to the front bench. The DCMS hopes to present its ideas to Number 10 shortly afterwards.
Design champions were set up after the 1997 general election as a way of securing better design quality in government buildings. Since then, Falconer has moved across government departments, working on the Millennium Dome and currently at the Department for Constitutional Affairs.