BRUSSELS/FRANKFURT/ROME, May 16 (Reuters) - Lufthansa has offered to keep some competing ITA short-haul routes in an effort to secure EU antitrust approval for its bid for a stake in the Italian airline, people with direct knowledge of the matter said on Thursday.

The offer is part of a package of remedies submitted to EU competition enforcers last week to allay concerns that the deal could reduce competition on short-haul and long-haul routes connecting Italy with other countries and ITA's dominance at Milan Linate airport.

Lufthansa wants to buy a 41% stake in state-owned ITA, the successor to Alitalia.

The offer on short-haul routes concerns Germany, Belgium, Switerland and Austria, the sources said.

A Lufthansa spokesperson declined to comment.

The German airline is also prepared to accept interlining agreements with rivals, the sources said. Such deals allow individual airlines to handle passengers travelling on itineraries that require multiple flights on multiple carriers.

To address EU concerns on long-haul routes, the German carrier said it would not integrate ITA into its joint venture with United Airlines and Air Canada, the sources said, adding that ITA would operate independently for two years.

Lufthansa also offered to give away 40 Milan Linate airport slots to easyJet and Volotea, they said.

The European Commission, which is scheduled to decide on the deal by July 4, is seeking feedback from rivals, consumer and travel organisations and pilot groups. They have until May 19 to respond. (Reporting by Foo Yun Chee Editing by David Goodman)