The talks come ahead of a key EU leaders\' summit in Brussels
In a major speech on the economy on Thursday, Mr Sarkozy said Europe had to be \"refounded\".He also said he wanted a new treaty to impose financial discipline on Eurozone
Britain is concerned about the possible impact of a reorganisation which could marginalise its influence in the EU.
The two leaders will discuss plans to reorganise the governance of the eurozone which will see closer co-operation within the 17-strong bloc, potentially lessening Britain\'s influence.
The move will be considered by the European Council at the end of next week, but Germany and France will agree a plan of action on Monday.
Any reforms of the Maastricht Treaty rules governing the eurozone will have to be agreed by all 27 members of the European Union.
\'Supportive and constructive\'
The talks come ahead of a summit of European Union leaders in Brussels next week, which is seen by many analysts as a crucial moment in efforts to tackle the debt crisis.
BBC correspondent Christian Fraser says Mr Cameron is under pressure from Conservative backbenchers and will seek to explore what Britain might get in return for its support.
But the next few days are critical to the survival of the single currency and our correspondent says it is unlikely Mr Cameron will want to slow down agreed eurozone changes.
Chancellor George Osborne warned MPs this week that, while Britain was not yet heading for recession, further crisis in the eurozone could pull the UK economy under.
On Thursday Bank of England governor Mervyn King said the Bank was making unspecified \"contingency plans\" in case of a eurozone break-up.
He said banks should brace themselves to withstand the \"extraordinarily serious and threatening\" economic situation.
In his speech in the port of Toulon, Mr Sarkozy said France and Germany must come together to ensure stability at the heart of Europe.
Mr Sarkozy said the euro could not continue to exist unless eurozone economies pulled together.
Mr Sarkozy and German Chancellor Angela Merkel are due to meet on Monday to propose measures to \"guarantee the future of Europe\", Mr Sarkozy said.
Downing Street said it was waiting to see the options paper for reform which European Council president Herman van Rompuy is drawing up for next week\'s gathering of EU heads.
Mr Cameron\'s official spokesman said: \"Primarily what is being looked at here is rules for the eurozone.
\"As with any negotiation in Europe we have to wait and see what is being proposed and see how we will respond.
\"We will always look to further our national interest.\"