The franchise contract is due to run out on Sunday, and both sides have agreed in principle that Virgin can run the route for a further 13 months.
But the department has not yet signed off the financial and legal terms of the extension, and remains in talks with the company to thrash out the final elements of the deal.
The extended contract is needed because the DfT scrapped a decision to award the route to rival FirstGroup in October, after uncovering major errors in the franchising process.
A report by Centrica boss Sam Laidlaw into what went wrong at the DfT has been completed, though it is not clear whether his findings will be published in full.
Laidlaw, who is also a non-executive director at the DfT, is due to appear before the transport select committee tomorrow to answer questions on the collapse of the West Coast franchise.