The former Brexit minister set a deadline of Monday – the day nominations close – for the other MPs to support a blueprint drawn up by the European Research Group.
The plans contained in the ‘Clean Managed Brexit’ document would do away with the Irish backstop and ensure that the UK leaves the EU by 31 October on World Trade Organisation terms if necessary.
Mr Baker said the next Prime Minister will face a moment of “death or glory” and must be ready to force Brexit through against the will of Parliament.
Speaking at the launch of the ERG plan, he said: “If we get to the opening of nominations on Monday and we collectively agree that there must be somebody who is willing to do this then I will be willing to be the person who gets nominated.”
Mr Baker heaped praise on Brexiteer leadership candidates Boris Johnson, Dominic Raab and Esther McVey – all of whom have promised to take the UK out of the EU on 31 October deal or no deal – saying the party was “spoiled for choice”.
“But I’m sure as a result of this stake in the ground we will have a range of conversations in the next few days and I will find myself in the hands of my colleagues,” he added.
“But if you are asking am I decided that if they ask me to do it I will, you bet.”
Mr Baker said a new Prime Minister should push the no-deal plan and “dare” MPs to bring the Government down in a confidence vote.
“I would recommend that a leader be absolutely committed in a resolute way to telling MPs: this is my policy, I’m asking you to back it,” he said.
“I did go through some training on this. In moments of death or glory you tell people what you are doing – you don’t participate.”