BRUSSELS, July 27 (Reuters) - Alstom is set to gain EU antitrust approval to buy Bombardier Inc's rail business, people familiar with the matter said on Monday, a deal which will make the French rail maker the world's second largest behind Chinese leader CRRC Corp.

Alstom earlier this month offered to sell a French rail factory, its regional train unit Coradia Polyvalent, and a Bombardier commuter trains division and the related production facilities at its Hennigsdorf site in Germany.

The French TGV high-speed train maker also proposed providing access to some products within Bombardier's train control systems and signalling units to rivals.

The concessions came after the European Commission voiced concerns about Alstom's greater market clout after the deal.

Alstom subsequently improved the concession on access to the Canadian company's train control systems and signalling units but did not have to sell more assets following feedback to the Commission from rivals and customers, the people said.

The Commission, which is scheduled to decide on the deal by July 31, declined to comment. Alstom and Bombardier also declined to comment.

Last year, EU regulators blocked Alstom's attempt to merge rail assets with Siemens AG after they refused to offer more concessions. (Reporting by Foo Yun Chee, additional reporting by Gwenaelle Barzic in Paris and Allison Lampert in Montreal; editing by Jonathan Oatis, Marguerita Choy and Sonya Hepinstall)