The Home Secretary dispatched officials to Denmark last month to study its border control and asylum policies, which are seen as some of the toughest in Europe.
Denmark's tighter rules on family reunions and restricting some refugees to a temporary stay are among the policies being looked at.
MPs from the governing Labour party in the UK are split on the move.
Some in so-called red wall seats, which are seen as vulnerable to challenge from the Reform UK party, want ministers to go further in the Danish direction.
Others believe the policies will estrange progressive voters.
It comes after a difficult few months for the government which has had to deal with rising numbers of small boat crossings in the English Channel and a migrant, who was deported under the UK's returns deal with France, re-enter the country.
The Home Office said on Wednesday that the Iranian man had been sent back again after he arrived in the UK for a second time on October 18, a month after he was initially removed.
But his second crossing back to the country prompted criticism that the government is in "total chaos" while ministers insisted his detection on arrival "shows the system is working".
On Friday, 648 migrants crossed the Channel to the UK in nine boats, Home Office figures stated, bringing the total for the year so far to 38,223.
Mahmood wants deterrents in place to stop people seeking to enter the country via unauthorised routes, while making it easier to remove those who are found to have no right to stay in the UK.
Sources said she was eager to meet her Danish counterpart Rasmus Stoklund - Denmark's immigration minister and a member of the Social Democrats - at the earliest possible convenience.
Labour MP Gareth Snell told BBC Radio 4 that any change bringing "fairness" to an asylum system that his constituents "don't trust" is "worth exploring".
He said it was "worth looking at what best practice we can find from our sister parties around the world where they have managed to find practical solutions" to managing immigration.
But fellow Labour MP Nadia Whittome, who is a member of the party's Socialist Campaign Group caucus, urged against emulating the Danish model.
"I think these are policies of the far-right. I don't think anyone wants to see a Labour government flirting with them," she said.
Stoklund likened Danish society to that of "the hobbits in the Lord of the Rings" and said people coming to the country who do not contribute positively would not be welcome.
"We are a small country. We live peacefully and quietly with each other. I guess you could compare us to the hobbits in the Lord Of The Rings," he said.
"We expect people who come here to participate and contribute positively, and if they don't they aren't welcome."
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