The Chinese firm specialises in skyscrapers and is believed to have held talks with main contractors currently chasing the job including Laing O’Rourke, Mace, Skanska and Sir Robert McAlpine.
Yuanda’s main rival for the job is German firm Gartner which was on board before British Land stalled the scheme due to the recession.
A winner for the main contract is due to be announced this summer ahead of main construction work starting on the tower later this year.
The Cheesegrater would be Yuanda’s first skyscraper in the UK but the firm has worked on a string of smaller contracts including the Park Plaza hotel in Westminster and ongoing jobs at Snow Hill in Birmingham and the Thames Gateway.
Cladding is seen as a market where Chinese firms can exploit the current lack of competition in the UK market.