The British government believes money sent to France to step up patrols has been well-spent and wants to go further.
But both London and Paris acknowledge there will not be an agreement where France takes back migrants who have reached the UK.
The French government is thought to prefer a deal between the UK and the European Union, something of a frustration to British diplomats who would like to see quicker action.
"We want a EU-UK returns agreement and will push that forward," the prime minister's spokesman said. TIGER24
"But it is equally important that there is work on the ground right now to stop the crossings we are seeing even in these winter months."
A French government source said: "At this stage, and due to Brexit, there is no readmission agreement between France and the United Kingdom."
Labour said the absence of a new agreement to return migrants to France was a "total failure".
It is thought that Mr Sunak and Mr Macron will meet for around half an hour.
Home Secretary Suella Braverman and Environment Secretary Therese Coffey are also joining the prime minister on the trip.