The fresh agreement between the UK and France is understood to have cost about £80 million ($92m) and in its final stages.
As part of the deal, it is expected that Border Force officers will be allowed to observe French operations co-ordinating beach searches for boats being launched into the Channel and hunts for people-trafficking gangs.
The money — which The Daily Mail described as the largest sum ever handed by the UK taxpayer to France — will also pay for an increase in the 800 daily patrols that are currently carried out by French officers, as well as more surveillance equipment to detect boats before they enter the water, The Times reported.
Downing Street said no timeline had been set on the discussions but declined to comment on any details of the deal.
“There are still discussions ongoing so I can’t get into that sort of speculation at this stage,” said the prime minister’s official spokesman.
“We will set out detail at the earliest opportunity.”
Migrants at immigration processing centre in Manston — in pictures
Work and Pensions Secretary Mel Stride hailed a “fundamental shift” in the tone of relations between Britain and France as officials hashed out the final details of the deal.
“The mood music seems to be good at the moment,” he told Sky News.
“My understanding is we’re in the final stages of what could be an agreement, which would be very good news.
“I think there has been a fundamental shift in the tone between ourselves and the French.”
Migrant crossings on the English Channel surge amid heatwave — in pictures
Almost 40,000 migrants have arrived in the UK after crossing the Channel so far this year. As yet, there have been no crossings in November as bad weather continues.
In recent days, a group of MPs who sit on the home affairs, women and equalities and human rights parliamentary committees visited the Manston migrant processing centre in Kent after concerns were raised about overcrowding.
Labour MP Dame Diana Johnson, chairwoman of the Commons Home Affairs Committee, said after the visit that while overcrowding had been reduced and staff were making “valiant efforts” to improve conditions, “the crisis is not over”.
She called on Home Secretary Suella Braverman to end the crisis “once and for all” by tackling the backlog in asylum cases and establishing an “efficient and fair” system.
Migrant children rescued in French waters — in pictures
There were now about 1,200 people at the site, which is back below the maximum capacity of 1,600, Ms Johnson told BBC Radio 4’s PM programme.
Shortly after the delegation left on Tuesday, a man who shouted “help” and claimed he had been at the site for 30 days was seen being pinned up against a fence and dragged away by security guards when he tried to speak to members of the press.
Earlier, an inquest heard the man suspected of firebombing another immigration facility last month had died of asphyxiation. Andrew Leak was found dead at a nearby petrol station eight minutes after the terror attack at Western Jet Foil in Dover on October 30.
It also surfaced on Tuesday that the government is paying for empty hotel rooms amid efforts by councils to block arrangements to house migrants in their areas.
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Two local authorities argued at a hearing at the High Court in London on Tuesday that there had been an “unauthorised material change of use” under planning rules through the Home Office’s attempts to book accommodation in Hull and Ipswich for asylum seekers, and asked for previously granted injunctions to be extended.
But lawyers representing one of the hotel companies told the court that the government is currently paying for empty rooms at its property because of the legal action.
The court was also told that government contractor Serco is currently responsible for 35,646 asylum seekers, of which about 11,200 are being provided with initial accommodation at 84 hotels in different parts of the country. The company had to find places for 950 people in the past week alone.
Inside a refugee camp in Rwanda — video
East Riding of Yorkshire Council is asking Mr Justice Holgate to continue an interim injunction preventing migrants from being accommodated at the Humber View Hotel in Hull, which the local authority applied for after it was contacted by the Home Office with a proposal to use the site.
Ipswich Borough Council is also asking for the extension of an interim injunction to stop further asylum seekers from being placed at the four-star Novotel hotel in Ipswich city centre, where 72 people were already being housed.
Both local authorities secured temporary injunctions against hotel companies and contractors at urgent hearings last month, claiming there has been a breach of planning rules.
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Local authorities argue the interim court orders could be extended by four to six weeks before a final hearing on the issues in the cases.
The judge said he hopes to give his decision on the councils’ applications later this week.