The latest offer came after the European Commission indicated an earlier proposal to sell warehouses and customer bases in about 15 countries, mainly in eastern Europe, was not sufficient to address competition concerns.
The world No. 1 package delivery company is seeking to buy Dutch peer and European market leader TNT to gain access to TNTs network in the fast-growing Asian and Latin American markets.
UPS submitted its latest offer to the European Commission on Monday, one of the sources said.
The remedies are substantially improved, the second person said, declining to provide details because of the sensitivity of the matter.
The EU antitrust authority, which will decide by February 5 whether to clear the deal, has told UPS rivals and customers to provide feedback on the latest concessions by Wednesday, one of the people said.Both the Commission and UPS declined to comment.