The Trade Minister said it would not bother him if the transition period was extended by “a few months”.
Mr Fox also slammed the Foreign Secretary who is eager to leave the EU and warned Theresa May not to allow the process of leaving to drag on.
Boris Johnson had said: “We don’t want some bog roll Brexit – soft, yielding and seemingly infinitely long.”
But Mr Fox said he would be happy to let the process roll on a little longer if it means making a clean break.
He said: “What I wanted was that we were outside of the single market, the customs union and the European Court of Justice.
“That’s where I think we’re going to end up.
“If we do it slightly more slowly in order to minimise any disruption, that’s fine by me.
“Having waited 40-odd years to leave the European Union, a few extra months doesn’t bother me if we‘re getting it right.”
The minister was adamant an extension to Article 50 to keep the UK in the EU after March 29 would be “politically unacceptable”.
However, on the second anniversary of the UK voting to leave the EU, he said prolonging the implementation period beyond 2020 would not be an issue.
Mr Fox said: “If the transition period had to be extended for technical reasons with the backstop and we already had the withdrawal agreement and future economic partnership agreed, I wouldn’t have a major problem with that.”
He added any extension must be “very time-limited” and there must be a way for the UK to opt out if we are being kept in the bitter bloc against our will.
The clash between the two Tory frontbenchers comes ahead of Theresa May’s trip to Brussels this week for her first showdown with EU chiefs since she fought off Brexit rebels to get the Withdrawal Bill passed through Parliament.
Mr Fox warned EU negotiators would be unwise to think Mrs May is “bluffing” about the possibility of a ‘no deal’.
He said: “The Prime Minister has always said that nothing is agreed until everything is agreed and that no deal would be better than a bad deal.
“I think it’s essential, as we enter the next phase of the negotiations, that the European Union understands and believes it.
“Our negotiating partners would not be wise if they believed that the Prime Minister was bluffing.”
The Tory also said the economic impact on countries in the EU would be severe if they failed to strike a deal.
However, he said remaining in the single market would be unacceptable because it would imply a continuation of free movement of people and would also mean remaining under the jurisdiction of the European Court.