By Christoph Steitz and Tom Käckenhoff
The firms, which have been working for three years on a deal that would create Europe's second-biggest steelmaker, submitted proposals to the European Commission on Monday aimed at addressing its concerns over the deal's impact on competition.
Thyssenkrupp Chief Executive Guido Kerkhoff, who is currently trying to break up the elevators-to-submarines conglomerate, has in the past said it would not be a disaster if the joint venture did not go ahead.
The Commission has until June 5 to review the firms' proposals and make a decision.
The source said the companies' concessions included selling two hot-dip galvanising plants in Spain and Belgium that supply the automotive industry.
They also proposed selling packaging steel activities operated by Tata Steel in Britain and Belgium, the source said, adding the Commission had dropped its concerns in the area of electrical steel.
"The offer is extensive and substantial. At the same time, it is acceptable to the joint venture partners and no risk to the industrial logic of the joint venture," Kerkhoff said in a statement on Tuesday.
Thyssenkrupp declined to comment on the contents of the proposal. Tata Steel was not immediately available for comment.
The source said the groups would not make far-reaching concessions that would question the entire joint venture, which was set up to reduce overcapacity and create a stronger and more competitive player.
Along with packaging, automotive steel has been one of the areas of competitive concern for the Commission.
A second source with direct knowledge of the matter said selling Galmed, Thyssenkrupp's hot-dip galvanising line in Spain, would not be enough to win over the Commission as it also has concerns in markets such as Germany, France and the Benelux countries.
The planned joint venture is targeting 400-500 million euros (343.41-429.26 million pounds)in annual synergies, a goal that would still be achievable under the proposals made on Monday, the first source said.
Overall, the assets offered for sale account for a low single-digit percentage of the joint venture's pro-forma sales of 17 billion euros, that source added.
Thyssenkrupp and Tata Steel could limit the field of potential buyers, which might include Salzgitter and ArcelorMittal, to industry players, the source said, adding materials supply contracts could be an added incentive.
(Additional reporting by Foo Yun Chee in Brussels; Editing by Kathrin Jones, Keith Weir and Mark Potter)
By Christoph Steitz and Tom KÃ¤ckenhoff