MP Kevin Hollinrake is supporting Michael Gove to be the next Prime Minister.
The Filey MP who had always voted in favour of Theresa May's deal said: "I've worked with Michael Gove for two years, he has the right skills to do the job and is somebody who campaigned for Brexit.
"I think that sometimes when there's something wrong with a plan you have to put it back to its original architect to make the repairs required so in this case I think it's Michael Gove."
According to Mr Hollinrake, the right way to leave the EU is with a deal and the first thing the Environment Minister should do – should he become the next PM – is go back to the negotiating table.
He added: "I think the deal we had was a sensible deal but it needs some changes. Michael Gove or anyone else should get over the channel, point out the difficulties of a no deal Brexit which is in everyone's interests to avoid and come out with a better deal.
"I don't think no deal should be taken off the table because it provides some imperative but we need to be an awful lot better prepared and have some contingencies in place."
However, the MP admitted that exiting the EU in an orderly way by the current deadline might not be possible, adding that candidates who promised to "to take us out of the EU by October 31 no matter what" have taken an "irresponsible position".
"The new Prime Minister is expected to be elected by July 22 but the next meeting of the European Council won't be until October 15.
"The negotiating teams will remain in place but nothing can be officially ratified until October 15 so the timescale is quite challenging but as long as the direction of travel is positive I don't think it will matter if it takes us an extra few weeks to get there."
The Conservative Party leadership contest, which officially kicks off today, is expected to take around six weeks.
The other Tory MPs standing for election are Boris Johnson, Jeremy Hunt, Andrea Leadsom, Sajid Javid, Rory Stewart, Dominic Raab, Matt Hancock, Esther McVey, Mark Harper and Sam Gyimah.