The Commission for Architecture and the Built Environment, which is to make the appointment, is believed to be in talks with Falconer over the job.
If he is given the post, Falconer will oversee the ministerial "design champions" appointed by Whitehall departments.
CABE declined to comment on the appointment, but it is understood to have been impressed with Falconer's views on the built environment and his commitment to improving delivery in the planning system.
In a letter to government departments in the spring, CABE said it was looking to appoint an "enabler" to oversee and assist the work of the design champions.
Meanwhile, some departments are employing their own advisers to help them with design. Former CABE commissioner Ian Ritchie took up this role for the Lord Chancellor, Lord Irvine of Lairg, at the beginning of this month.
CABE's connection with the Lord Chancellor's department is likely to be formalised by a partnership agreement. This would mean that the commission would have an advisory role on court PFI projects.
The arrangement would be similar to CABE's partnership deal with NHS Estates, by which the commission offers developers and public sector clients advice on procurement and the choice of architects before schemes are submitted to the planning authority.
CABE has worked extensively with the Lord Chancellor's department in the past, and has convinced it to include design as a separate stage in the PFI bidding process.
Their latest project is a £16m, 25-year PFI contract, due to be announced today. The Court Service has shortlisted two consortiums: one includes Mowlem and Innisfree Management; the other comprises Norwest Holst and McBains Investment Management. The winner will build eight courts in Ipswich and Cambridge.
A source confirmed that CABE had "been invited" to advise both sets of bidders on their design plans.
Members of the eight-strong design in construction alliance will include representatives of the Construction Industry Council and the Major Contractors Group.
Sir Stuart Lipton, chairman of the commission, said: "It's time for design and construction to promote a united front to government and to industry so that those changes result in higher quality buildings."