The government is poised to announce a new “safe and legal route” to the UK for 20,000 migrants each year.
Reports suggest the new scheme will be enshrined in the UK's new Migration Bill, which is designed to put a stop to migrants crossing the English Channel in small boats.
The government previously said it needs to get a grip on illegal migration before establishing any more legal routes.
But moderate Conservative MPs, led by Tim Loughton, believe the limited number of existing arrangements is not sufficient.
Mr Loughton, who sits on the Home Affairs Select Committee, told The Telegraph the government's current plan to wait until the small boats problem had been addressed “just won’t wash”.
And he said new legal routes “need to be in place before the legislation comes into force. And he warned they must be “meaningful” new routes, rather than an “elaboration” of existing ones.
Mr Loughton's group had planned to table an amendment calling for the inclusion of a new safe route to the controversial legislation, which returns to the House of Commons for its committee stage on Monday.
But reports suggest the Prime Minister could be about to back down.
Rishi Sunak is facing objections to the terms of the bill from two wings of his party, both the liberal and the right.
The liberal amendment, backed by a number of moderate Tory MPs, also reportedly has the support of Labour, which could have resulted in a defeat for the government.
There are currently few legal avenues for migrants to enter the country, with schemes in place for people coming from Afghanistan, Ukraine and Hong Kong. The country also offers reunion visas for refugee families, as well as a more general resettlement scheme.
A separate challenge has been mounted by other Tory MPs who believe the bill does not go far enough.
Speaking on BBC Radio 4 on Monday, Danny Kruger said: “We think we want it go a little further.”
He said: “We need to ensure that what happened last June doesn’t happen again, which is parliament passed a law to ensure people who arrived here illegally should be swiftly removed.
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“And the European Court of Human Rights, literally in the middle of the night, by an unnamed judge, issued an interim order, which effectively stopped the removals taking place.
“The bill that now is in front of parliament is very, very good. It tightens up the existing law significantly and we are entirely supportive of it. But we think there are some improvements that need to be made to ensure that doesn’t happen again.”
He said people should only be prevented from being deported if they are unfit to fly or if they would be at risk of harm in the country they are being sent to.
“Those are the considerations that should apply. The only considerations that should apply that stop somebody from being removed,” he said.
Mr Kruger said he was “supportive of the principle” of opening up a safe and legal route for migrants to enter the UK.
“The corollary, the natural complement of the proposals … is to have proper safe and legal routes.
“We are taking well over [20,000] at the moment. We have taken hundreds of thousands of refugees in recent years. The cap is for parliament to discuss.
“But yes, it is right that we create proper safe and legal routes. But first we have to ensure that people who don’t come through those safe and legal routes should be removed.”
Mr Kruger said he had tabled amendments to the bill but was confident of getting commitments from the government to ensure the group of MPs wanting the legislation to go further would not have to “push them to a vote.”