The Indian firm said on Friday that it was in talks with its German competitor and other unnamed groups to create a large European steelmaker but did not give further details.
Tata has been considering seven bids for its UK assets since putting them up for sale in March, citing a global oversupply of steel, cheap imports into Europe, high costs and currency volatility.
"We have always said that we consider a consolidation in the European steel sector necessary due to the very difficult economic situation," Thyssen spokeswoman Nicola Roettger told AFP.
"The entire steel industry in Europe is fighting to continue to have a future in a difficult economic context," she said. "Very few European steelmakers are currently making profits," she said.
Koushik Chatterjee, group executive director and Tata Steel's executive director for Europe, said it was "too early to give any assurances about the success of these talks".
The British government has been racing to help find a buyer for Tata's business, which had accounted for about 16,000 jobs in total, many of them at the Port Talbot steelworks in Wales, the country's biggest steel plant.