"It is vital to see rebalancing within the euro area with surplus economies contributing more to demand," said the official, who asked to remain anonymous.
The official said the sluggish European economy had subtracted 0.3 percentage points from global economic growth in 2012.
Lew Monday was scheduled to meet with President of the European Council Herman Van Rompuy, European Commission President Jose Manuel Barroso, Commissioner of Internal Market and Services Michel Barnier and Finance Commissioner Olli Rehn.
On Tuesday, he was to meet with the finance ministers of Germany and France, Wolfgang Schauble and Pierre Moscovici.
Some finance ministers are concerned that the focus on reducing government debt is creating a cycle of poor economic performances followed by reduced tax revenues, which means further spending cuts would be required to maintain a strategy of lowering debt.
In the final quarter of 2012, the gross domestic products contracted in the eurozone's four largest economies -- Germany, France, Spain and Italy -- and in the eurozone as a whole.
Despite that, European leaders have repeatedly been disdainful of U.S. leaders flying to Europe to tell them how to fix their problems, which are widely considered to have begun with the 2008 financial crisis in the United States, the Times said.
German leaders have also steeled themselves in the past four years against European resistance to budget discipline. Germany is not likely to change course at Lew's suggestion.