Clifford Chance (CC) has moved a step closer to letting out six floors of empty office space in its City headquarters, with Transport for London (TfL) in talks to take the space.

The transport body has put in an offer to take over roughly 220,000 sq ft of CC's 10 Upper Bank Street building in Canary Wharf – equating to six of tower's 30 floors.

The offer, first reported by property website CoStar, has yet to be agreed by TfL's board, however if the deal does go ahead it will end a hunt for a tenant which has been going on for well over 18 months.

CC has been scrambling to fill the empty space since late 2012, after the London Organising Committee of the Olympic and Paralympic Games (LOCOG) moved out. The committee vacated the building in staggered lots in the months following the 2012 Summer Olympic Games.

While the space has been empty the firm has been missing out on millions in annual rental income, with property advisers CBRE and GVA's  respective websites listing rental rates on the building at £39.50 per sq ft. The magic circle firm appointed the pair to market the space in 2012.

If TfL were to agree to pay rent at this rate for all six floors it would bring in around £8.7m a year for CC. In comparison LOCOG took on 135,000 sq ft in the building, which it moved into in 2010.

TfL will reportedly start moving into the offices in September 2015, with some 3,000 staff to occupy 2,500 desks in the building.

Commenting on the news one CC partner said: "It's the first news we've had in a while on the subject. Having a subtenant would make a difference to our profitability and go a long way in reducing overheads. We've been trying to do something about this for a while, so we are keeping our fingers crossed there will be good news."

CC also sublets space in its building to MasterCard, InfoSys, Total and the FTSE Group.

London managing partner David Bickerton, who was re-elected to the leadership role last November, has been overseeing the search for new tenants.

TfL, GVA and CBRE declined to comment. A spokesperson for CC said: "It has always been our policy to market excess space at our 10 Upper Bank Street offices in Canary Wharf. We have a landmark building in a major business centre and often show prospective tenants around the building." The firm would not comment in relation to the discussions with TfL.

CC moved into the building in 2003, becoming the first UK law firm to take up residency in Canary Wharf.