Lawmakers were this week told to expect extra Commons sittings over the festive period in order for a Brexit trade deal to be passed. But Mr Peston said the additional sittings could be used to conduct last-minute preparations for a hard Brexit.
He responded to reports suggesting the Commons could sit early next week to vote on a deal with Brussels.
He said an extra meeting of MPs being scheduled would not necessarily mean a deal had been secured.
Mr Peston tweeted: “For those seeing the possibility of the Commons sitting on Monday and Tuesday as a sign a free trade deal with EU may be close, it is worth noting ministers were also warned today they may be working between Xmas and new year to prepare for no deal on 1 Jan.”
On Tuesday evening BBC Newsnight’s political editor, Nicholas Watt, said he had gotten wind of a possible deal between London and Brussels.
He said there was a “big buzz” among Tory MPs about an agreement which would keep eurosceptics satisfied.
He said MPs had been told, “the signal will come if and when Jacob Rees-Mogg announces that the Commons will sit on Monday and Tuesday next week.”
Mr Rees-Mogg, the leader of the House of Commons, on Tuesday, announced a change to parliamentary business but failed to confirm when the Commons will break for Christmas.
Making a statement to MPs, he said all stages of the Trade (Disclosure of Information) Bill will now be considered on Wednesday.
Mr Rees-Mogg said the Government is ensuring legislation needed before the end of the Brexit transition period can be approved by MPs.
He also said: “I did warn members last Thursday, as I thought it was only fair to do so, that we might have to act flexibly to developments in what is going on.”
Mr Rees-Mogg said, “there is no last moment” to secure a free trade deal with Brussels as he hinted at a possible last-minute agreement.
He suggested negotiations could continue “until Big Ben strikes 11 o’clock” on December 31.
The UK’s Brexit transition period will expire on New Year’s Eve.
In comments carried by the Independent, the Commons leader left the door open for a vote on a deal in 2021.
Mr Rees-Mogg said Parliament could be asked to “retrospectively correct” domestic law to recognise any agreement with Brussels.
But he admitted the move would be hugely controversial.
He said “if anyone took it to court I think you would find yourselves in considerable difficulties”.