However Steve Baker, the deputy chairman of the pro-Brexit Tory European Research Group, said it was the view of the Prime Minister which counted.
“Officials advise. Ministers decide. If the PM decides we are leaving on March 29, deal or no deal, that will happen,” he said.
A Downing Street source said: “Look at the facts. We are doing everything we can to get the meaningful vote delivered by the end of February.
“Parliament has set out very clearly that it wants this to be resolved by then. The Prime Minister wants this over and done by March 29.” Downing Street declined to comment on “alleged remarks from a private conversation”.
The Prime Minister was accused of running down the clock in a bid to “blackmail” MPs into backing her deal as she cleared a path to hold the Brexit vote just days before March 29.
Mrs May said she would lift a requirement that there must be a 21-day delay before a vote to approve an international treaty in a move that will allow the UK to leave the EU on time.
Earlier Andrea Leadsom, the Leader of the Commons, declined to rule out holding the Brexit vote in the week before Brexit.
She also raised concerns among Eurosceptic backbenchers after saying that they must not be “purist” by demanding a time-limit of backstop to the Prime Minister’s Brexit deal.