Irish Premier Bertie Ahern is expected to hold talks with the UK prime minister in Downing Street.
Tony Blair and Bertie Ahern will discuss the NI process
Both leaders are expected to discuss EU matters and touch on the latest developments in the political process.
Irish sources said the taoiseach would be pressing for progress early next year on the restoration of the devolved government at Stormont.
Mr Ahern met Tony Blair in October, with both leaders seeking ways to restore devolution in Northern Ireland.
At that time, Mr Blair said there had been "a genuinely significant change in the politics of Northern Ireland".
It followed a statement by the IRA in which it said it had put all of its weapons beyond use.