On Tuesday MPs will be asked to back legislation which the prime minister has said will see people seeking asylum in the UK sent to the east African country instead.
Sunak has made the policy a key part of his promise “stop the boats” in the run-up to the next election, after previous attempts were blocked by the courts.
The government hopes the threat of being sent to Rwanda will deter people from crossing the English Channel.
But Conservative MPs on different wings of the party have not yet decided whether to support the bill.
It would take only 29 Tory MPs to vote against the plan for Sunak to lose.
Speaking to Sky News’ Sunday Morning with Trevor Phillips, Gove was asked if this would cause the government call an early election.
“No we’re not contemplating that because I’m confident that when people look at the legislation - and have a chance to reflect - that they will recognise that this is a tough but also proportionate measure,” he said.
The levelling up secretary added: “Of course, we will listen to opinion within the House of Commons.”
The next election must be held by January 2025 at the latest, with May or October of 2024 seen as the most likely dates.
Tory MPs on the right have been awaiting the conclusions of a so-called “star chamber” of lawyers examining the legislation.
In a blow for Sunak, The Sunday Telegraph reported they have decided the bill is not “watertight” enough to stop asylum seekers launching legal battles against being sent to Rwanda.
Robert Jenrick, who quit as immigration minister last week in protest at the proposed law, said he would not be voting for it.
He told the BBC’s Sunday with Laura Kuenssberg programme it was a ““weak bill that won’t work”.
“I don’t believe this bill will work. I think it will lead to a range of legal claims which will bog down our scheme and will not create the deterrent that he and I set out to achieve,” he said.
Sunak is also facing opposition from more moderate MPs. Damian Green, who leads the centrist One Nation group of Tories, said they would meet on Monday to decide how to vote.
Green said MPs on his wing of the party were worried the legislation could break the “rule of law” and fail to live up to the UK’s “international obligations”.
The flagship Rwanda policy - first announced when Boris Johnson was still PM last year - has been beset by problems.
In November the Supreme Court ruled the original law was unlawful as there was a real risk of people deported to Rwanda from the UK being sent back to their home county where they faced persecution.