he British prime minister is aiming for closer Franco-British ties as he prepares to travel to Paris for the first UK/France summit in five years.
But the French president is expected to reject pleas for a bilateral returns agreement.
The UK government is known to want such a deal with Paris, which would allow London to immediately return those arriving in Britain unlawfully from France.
Labour said Mr Sunak will have failed if he goes back to the UK without a returns agreement.
Ahead of his trip, Mr Sunak expressed hope that the UK and France could build on the £63m (€70m) agreement announced in November to help prevent small boats crossings.
The Daily Express reported that Mr Sunak is ready to green-light a deal that would secure a multi-year migration agreement with Paris, which would include Britain paying millions of pounds to France every year to increase the number of patrol officers on French beaches.
He told reporters on Wednesday: “I was really pleased at the end of last year that we managed to announce the largest ever small-boats deal with France, which led to a 40pc increase of patrols on French beaches and increased co-ordination between our teams.
“So on Friday, hopefully, we can continue to strengthen and deepen that co-operation in those areas.
“More broadly, I think there’s a range of things that we want to work closely with our partners and allies on – whether it’s standing up to Russian aggression and supporting Ukraine, whether it’s improving our energy security, or indeed whether it’s illegal migration.”
Under the existing pact, the number of French officers patrolling beaches on the country’s northern coastline rose from 200 to 300, while British officers were also allowed to be stationed in French control rooms and to observe operations.
Elysee Palace sources have reportedly briefed that a new deal could be signed off on “strengthening” co-operation between the UK and France on managing the border through “multi-year financing”.
Clare Moseley, of refugee charity Care4Calais, said: “The reality is expensive deals with France will not stop people smugglers, they won’t end small boat crossings, nor will they keep refugees safe.
“There is a kinder, safer and more effective option – giving safe passage to refugees in Calais in a similar way we have for Ukrainians.”
The Franco-British talks come days after Mr Sunak and home secretary Suella Braverman unveiled the Illegal Migration Bill, which would see migrants who arrive in the UK through unauthorised means deported and given a lifetime ban on returning.
There are hopes today’s meeting will turn the page on years of post-Brexit tensions, with the Elysee seeing it as a “very important step” in the “recovery process” of relations.
An expected call between the two leaders, which was due on Monday, did not take place.
Labour’s justice spokesperson, Yvette Cooper, said: “Rishi Sunak will have failed if he comes back from the summit without a new returns agreement and new joint arrangements to prevent dangerous boat crossings.”