The UK government is in negotiations with France on a scheme to return illegal migrants who have crossed the Channel in small boats.
In return, the British government would accept legal migrants seeking family reunion in the UK.
The French interior ministry told the BBC this would be a pilot scheme based on "a one-for-one principle", with the aim of discouraging smuggling networks.
The Conservatives said Labour's decision to scrap the Rwanda deportation agreement last year had removed a deterrent to illegal immigration.
UK Transport Minister Lilian Greenwood said the government was talking to France about migration issues but did not comment on the possibility of a removals deal.
She told Sky News: "I can confirm that there are discussions ongoing with the French government about how we stop this appalling and dangerous trade in people that's happening across the English Channel."
The talks with France were first reported by the Financial Times.
"France's interest is to discourage migrants and smuggling networks from attempting to reach the UK from France," the country's interior ministry told the BBC.
The ministry suggested the pilot scheme could pave the way for an agreement on migrant returns between European Union member states.
"It is based on a one-for-one principle: for each legal admission under family reunification, there would be a corresponding readmission of undocumented migrants who managed to cross [the Channel]", a spokesperson for the ministry said.
In 2023, the previous Conservative government struck a deal to give France almost £500m over three years to go towards extra officers to help stop migrants crossing the Channel in small boats.
Conservative leader Kemi Badenoch said the previous government had multiple agreements, including with France and Rwanda.
The Rwanda scheme aimed to deter small boats crossings in the Channel by sending some people who arrived in the UK illegally to the east African country.
But the plan was stalled by legal challenges and Labour scrapped the scheme before any migrants were sent to Rwanda.
Badenoch said Labour's decision to drop the Rwanda agreement had removed a deterrent to illegal immigration.
"It's time that Labour got serious and stops making things easier for the gangs that are smuggling people across the Channel," she said.
Reform UK MP Lee Anderson said: "Instead of negotiating trade-style agreements concerning migrants, the focus should be on securing and closing our borders.
"Such a strategy would be more effective, less costly, and far simpler."
He added: "The priority must be reducing the number of illegal migrants in our country, not simply replacing them."
The Liberal Democrats and the Green Party have been approached for comment.
In 2023, Prime Minister Sir Keir Starmer said he would seek an EU-wide returns agreement.
But no such deal has come to fruition since Labour won the general election last year.
An EU-wide deal would be likely to face resistance from some European countries, such as Hungary, which has taken a hard line on migrants entering the country.
The UK government has so far focused on targeting people-smuggling gangs to bring down illegal migration, which is one of Labour's biggest challenges.
Earlier this year the government announced a series of measures to tackle people smuggling, including a new criminal offence of endangering the lives of others at sea with a jail term of up to five years.
Ministers have insisted there is no single "silver bullet" for solving the problem of illegal migration and the latest scheme is only one of a number of options being considered.
The latest Home Office data show more than 8,180 people are thought to have crossed the English Channel this year so far.
This was 31% higher than the same point last year (6,265), and 67% up from this stage in 2023 (4,899).
A Home Office spokesman said: "The prime minister and home secretary have been clear the UK and France must work closely together to prevent dangerous small boat crossings, particularly on vital law enforcement co-operation.
"We have already secured agreement from the French to deploy a new elite unit of officers at the coast, launch a specialist intelligence unit, increase police numbers and introduce new powers for the French authorities to intervene in shallow waters.
"We are intensifying our collaboration with France and other European countries who face the same challenges by exploring fresh and innovative measures to dismantle the business models of the criminal smuggling gangs."
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