The Financial Times said the commission will propose to EU finance ministers Tuesday that Spain be allowed to relax its deficit target for this year to 6.3 percent of its gross domestic product.
Prime Minister Mariano Rajoy, however, will have to commit to more tax increases, the newspaper said.
The Wall Street Journal said most of the 17 eurozone countries were in favor of giving Spain until 2014 to cut its government deficit to below 3 percent of the GDP.
A deal with the holdout countries is expected by Tuesday, the Journal said.
"There are proposals on the table that I think are of a nature to get consensus," French Finance Minister Pierre Moscovici was quoted as saying.