A source at one of the four bidders said he expected the decision to be made in weeks once talks between the government and the Greater London Authority were completed.
The GLA's Tube supreme Bob Kiley is due to meet deputy prime minister John Prescott next week to work out a compromise with the GLA's concerns over the project.
Confidence that the deal will go through is widespread, despite reports that two of the bidders for the main contracts are threatening to pull out. The tendering process is thought to have cost each consortium £15m so far.
Kiley, and London mayor Ken Livingstone, want the government to think again over how the scheme is to be financed. They believe that the GLA can fund the redevelopment by issuing bonds bought by the public, rather than through private sector loans. They also want to scrap a requirement that all stations be upgraded in the first five years of the 30-year contracts.
Firms were told to submit new lower bids for the schemes last month. These are expected to be submitted to the DETR today.
There is a lot of talking going on but I am quite sure that this is going to go ahead
Unnamed tube bidder
One bidder said he was confident that the decision would be made swiftly. He said: "There is obviously a lot of talking going on, but I am quite sure that this is going to go ahead. It's just a question of the parties talking it through."
The source said his team had not changed the substance of its bid but had revised the valuation.
Another bidder played down the influence of the GLA over the decision process. He said: "Kiley will not change the government's mind on this. He might change some of the terms and conditions of the contracts but it will still go ahead."
A source close to the bidding process supported this view. He said: "Some of the bidders are getting nervous because of what the GLA is saying. But this deal will be done whether the mayor likes it or not."
A GLA spokesman described the negotiations between Kiley and the DETR as positive and expressed confidence that an agreement would be found.