Prime Minister David Cameron is expected to press French President Francois Hollande to back European Union reform as he hosts a UK-France summit, reports the BBC.
The talks, which will take place at RAF Brize Norton, Oxfordshire, are expected to cover subjects including energy, defence and science.
A source said Mr Cameron would call for a "more flexible" EU during the lunch.
But a source close to Mr Hollande said he was unlikely to back such a move.
Mr Cameron's Conservative Party is promising to hold an in-out referendum on the European Union by the end of 2017 if it wins the 2015 general election.
This is unpopular among Mr Hollande's ministers, according to BBC Europe editor Gavin Hewitt, who said: "They will not accept a Europe a la carte, where countries cherry-pick what they like."
Read more of this report from the BBC.