Mr Peston made the remark whilst speaking to Tory leadership candidate Mark Harper. The former Foreign Secretary is the favourite to replace Theresa May as Prime Minister. Mr Johnson has insisted he will take Britain out of the EU on October 31 with or without an exit deal.
Addressing Mr Harper the ITV host said: “There is a risk given what Boris has said that he’ll be the shortest living Prime Minister in history.”
If Mr Johnson becomes Prime Minister and pushes ahead with a no deal Brexit pro-EU Tory MPs could force a General Election.
Conservative backbencher Dominic Grieve has said he would quit the Conservative Party if necessary to prevent a no deal exit on October 31.
Mr Harper replied: “I think there’s a risk there will be an early election and most of my colleagues in Parliament won’t want an early election.
READ MORE: Boost for Boris! Theresa May’s former right-hand man backs Brexiteer
“I understand why they’re saying it about leaving on October 31 deal or no deal but I think it’s a mistake.”
The Tory backbencher went on to argue the Government won’t be able to agree any new deal with the EU by October 31.
He commented: “I don’t think there’s a credible way that you can leave with a deal on October 31.
“New person will become Prime Minister in July. Most of Europe is on holiday.
READ MORE: Brexit bombshell – Commons can still block no deal EU exit
“There isn’t really a commission in place now until November.
“The chances of getting everybody around the table, agreeing a deal through both Houses of Parliament, simply isn’t credible.”
The first round of the Conservative leadership election will take place later today, with only Tory MPs voting.
Any candidate who doesn’t have the backing of at least 17 MPs will be removed from the contest.