Michael Cassidy, chairman of the City's planning and resources committee, and Sir Peter Levene, who heads Canary Wharf, are understood to have drafted a set of general principles setting out how they should compete for business.
If approved by their colleagues and the London Docklands Development Corporation, which also has an interest in where new office tenants go, the draft could become the basis of a formal protocol.
The plan is to put an end to public criticisms of each other's schemes and prevent cut-throat competition in the search for new tenants.
One feature of the likely accord, discussed at a meeting between the two men on Thursday, is thought to be an agreement that neither side sets out deliberately to cold-call existing businesses located in the other's area, to persuade them to move.
The City could exclude firms in Docklands from a forthcoming campaign to woo back organisations that have left London over the past decade.
The move comes after a long period of tension between the Square Mile and Docklands which erupted publicly earlier this month when BZW, the Barclays subsidiary, announced it was moving 1,800 staff to Canary Wharf. Mr Cassidy claimed BZW would lose 40 per cent of its staff and said the extra pay to compensate them for the move was likely to cost BZW the equivalent of £5 a square foot on the rent.
Canary Wharf, which has attracted tenants by offering big rent concessions, has been claiming office building costs half as high as the City.
BZW's decision to move into an existing building at Canary Wharf alarmed the Corporation, which is now concentrating efforts on keeping the London International Financial Futures Exchange inside the City boundaries when it moves to new and larger premises in a few years. The City has given Liffe the services of a planning officer and a surveyor to help find a site.
But Liffe has identified ways to expand capacity on its existing site and postpone a move of its trading floor for up to eight years, giving more time to find a solution within the City. No existing building will accommodate it, so a new development is required. Mr Cassidy said yesterday of his meeting with Sir Peter: "We made good progress."