The council declined to reveal who is in the running, but it is understood that Bovis, Amec, Laing, Mowlem, Taylor Woodrow and HBG have been shortlisted.
The firms were due to receive tender documents for the project this week, ahead of the 7 March return date. A project source said the council would pick a contractor for the Arup Associates-designed stadium on the basis of track record and local market knowledge.
Meanwhile, the council this week denied weekend reports that it needs to ask the government for extra funding for the 2002 Commonwealth Games on top of a £112m Sports Council lottery grant.
A spokeswoman said: "Everything is going in the right direction. We are emphatic that we do not need to go back for more money." She said the stadium would swallow up £77m of the lottery grant – with an extra £13m coming from council resources – and that a tennis centre and a sports academy would cost a further £13m.
With sponsorship expected for team sports such as cricket and rugby, the council says a new business plan, to be completed in April, would allow the games to be staged without extra funding.
Last week, at a local government conference in Manchester, this point was reinforced by prime minister Tony Blair, who wished the games good luck, but reaffirmed that no extra cash would be available.
The stadium is due to start on site at Eastlands in September, with construction of a 40 000-seat facility due for completion in late 2001.
After the games, its capacity will be increased to 48 000. Heads of terms have been agreed for second division football club Manchester City to then take over the stadium. The club's Maine Road ground on the other side of Manchester is rumoured to have been earmarked by a major North-west rugby union or rugby league club as its new home.
Weekend press reports suggested that the cost of running the games had soared and that the event was already projected to make a £5m-10m loss.
However, the council said this speculation was based on eight-month-old figures and that sponsorship is expected to take off soon. Manchester Airport has already pledged £2m and the council will soon name a company that will pay to televise the games.