The Home Secretary will travel to Paris to meet her French counterpart amid growing fears the French could axe British border controls in Calais and send the Jungle camp to Dover.
Amber Rudd is due to discuss security with French Interior Minister Bernard Cazeneuve during the scheduled trip on Tuesday - her first official overseas engagement since taking up the post.
It comes after a growing number of prominent French politicians have warned that France might tear up the deal which allows British border checks to be carried out in Calais unless radical changes are made.
Xavier Bertrand, president of the Hauts-de-France Nord Pas De Calais-Picardie region which includes Calais, told the BBC Radio 4 Today programme he wants a "new treatment" for asylum seekers trying to get to Britain from France.
He said: "If the British Government don't want to open this discussion, we will tell you Touquet Agreement is over."
Under the Treaty of Le Touquet, British immigration officials check passports in Calais and their French counterparts do the same in Dover.
But the sprawling Calais migrant camp, where thousands live in filthy conditions and each night try to smuggle themselves across the Channel on board lorries heading for Britain, has become a source of resentment among the French.
Mr Bertrand wants a new deal in which migrants hoping to claim asylum in the UK would be able to do so at a "hotspot" in France. Those who failed would be deported directly to their country of origin.
This would be a radical departure from current rules known as the Dublin Regulation which states that refugees must register in the first European country they arrive in. This country usually takes charge of their asylum claim.
Nicolas Sarkozy, the former French leader who is running for his party's nomination for next year's presidential race, has called for the opening of a centre in Britain to deal with the asylum seekers.
But Sir Peter Ricketts, the former British ambassador to Paris, said the proposals to create hotspots risked attracting thousands more migrants to France.
He said: "As soon as you suggested that, there would be a huge magnet pulling thousands and thousands more migrants into Calais to chance their arm, make an asylum claim, hope that they might get to the UK and good luck."
He also warned the entire asylum system is under "huge pressure" and said that if the Right win next year's presidential election "the British Government is going to have to deal with a pretty serious conversation about the future of the Le Touquet Agreement".
Charlie Elphicke, Conservative MP for Dover, told the Press Association axing the treaty "would simply not work" and instead it should be strengthened so migrants can be efficiently registered and either given asylum or sent back to their homeland.
He said: "For too long the symptoms have been addressed with big fences, we need to deal with the actual causes and to deal with the Jungle which is a magnet for migrants, and deal with the people traffickers who are selling stories of how they ought to go to Britain."
He said he has sent Mrs Rudd two reports, one calling for the Royal Navy to create a new Sea Marshal force along the south coast to intercept people smugglers and another urging the dismantling of the Jungle.
A Home Office spokesman said: "We remain committed to working together to protect our shared border in Calais and to maintain the juxtaposed controls.
"The French government has repeatedly made it clear that removing the juxtaposed controls would not be in the interests of France."
He added: "We firmly believe in the established principle, enshrined in the Dublin Regulation, that those in need of protection should seek asylum in the first safe country they enter."
Tim Farron, leader of the Liberal Democrats, said: "The French and British governments have both failed to deal with the pile up of refugees in Calais over the last year, and we're now facing the consequences of that failure.
"But Sarkozy with his desperate little speech at Le Touquet is trying to grub around in the gutter for votes to win his presidential primary. It won't work and trying to mimick the nasty rhetoric of Marine Le Pen is not a recipe for success. He just looks like a hypocrite.
"Theresa May should use the upcoming G20 to seek reassurances from the French government about the deal that Sarkozy himself actually signed in 2003."
Meanwhile it was reported Britain is threatening to review security co-operation with France if it tries to scrap the border arrangements in Calais.