The top-15 practice is understood to be independently auditing the costs of the delayed scheme for client the Football Association.
If the costs are given the all-clear, the scheme is likely to be given government approval by the end of April – nearly a year after design work stopped on the scheme because of a funding crisis.
Cyril Sweett refused to comment on its appointment, but sources close to the development claimed its role would be to allay fears over the feasibility of the project. One source said: "The government and the FA want to satisfy themselves that it all stacks up. People have been very twitchy about this project."
Government spending watchdog the National Audit Office, which has been advising the government on the financial feasibility of the scheme, confirmed this week that an external firm was looking at it.
A spokesperson said the FA wanted to reassure the government over the cost of the project, and that it would be properly managed by Wembley National Stadium Limited, a subsidiary of the FA.
The government and the FA want to satisfy themselves that it all stacks up
Source close to the project
In January, Building revealed that the board of WNSL would be shaken up to include more directors with private sector experience.
The government and the FA approved a scaled-down version of the original Foster and Partners/HOK Sport-designed scheme in December.
The new appointment came as Australian contractor Multiplex confirmed this week it was near to confirming its team of specialists for the project, including demolition, steel and M&E contractors.
A Multiplex spokesperson said: "We are in advanced and detailed negotiations with contractors. The contractors will be in place when we reach financial close in April."
Sources close to the project said the appointment of the steel contractor, expected to be won by William Hare, had been delayed. This was due to the acquisition of Hare's partner for the scheme, Watson Steel, which was bought from Amec by Severfield Rowen last year.