Talks to appoint Burdett, who was curator of September's Venice Architecture Biennale, could be read as a bid to deflect growing criticism of the ODA's controversial procurement and architecture strategy.
It is understood he will join the organisation on a two-day-a-week basis to advise it on architecture and design.
Burdett, who is one of the most significant players in London's architecture scene, will hope to counter growing disenchantment with the ODA's perceived commitment to Design and Build contracts.
Burdett rose to fame as the original curator of the Architecture Foundation before he joined the London School of Economics to set up the successful Cities Programme.
Ironically, it was Burdett's boss at the mayor's Architecture and Urbanism Unit, Richard Rogers, who last month made the most vocal attack on the ODA to date ( Rogers voices fears over Design and Build Olympics).