Contractor Amec is also considering a bid. It is expected to discuss putting together a consortium today.
Amec and Bovis Lend Lease are thought to be part of a relatively small field of potential bidders.
Many firms have been put off because of the size of the project – it is three times larger than most PFI hospital schemes.
The country's biggest health scheme, the £620m Royal London and St Bartholomew's hospitals, attracted only two bidding consortiums, led by Bouygues and Skanska/Innisfree.
Earlier this year, Bovis Lend Lease is thought to have considered pitching for the Bart's scheme.
The project is integral to the wider, £3.5bn urban regeneration of England’s second city, and crucial to environmental and economic development
Hospital outline business case
Sources close to Bart's believe it decided against doing this so that it could concentrate on the Birmingham project.
The Birmingham scheme involves the design, construction, financing and operation of a teaching hospital and mental health facilities at the Queen Elizabeth Medical Centre campus.
The project is earmarked for completion by 2007/8 and will be Birmingham's first hospital for more than 60 years.
An advertisement inviting expressions of interest from potential bidders was placed in the European Union's Official Journal earlier this month. In the advertisement, the Birmingham NHS Trust said it expected to invite between two and four consortiums to tender.
The trust believes the project is a key part of the regeneration of the city. In an outline business case, published earlier this month, the trust said: "The project is integral to the wider, £3.5bn urban regeneration of England's second city, and crucial to the environmental and economic development of the A38 technology corridor in the south of Birmingham."