German carmakers BMW, Mercedes-Benz and Volkswagen are in talks with the U.S. Department of Commerce on a tariff deal that would involve a mechanism to offset imports and exports, the Handelsblatt business daily reported Wednesday.

In return for tariff relief, the companies could invest billions in the United States, the report said citing company sources. It did not give a more exact sum.

The aim is to clinch a deal by early July, according to Handelsblatt.

BMW declined to comment. Volkwagen and Mercedes were not immediately available when contacted by Reuters. Handelsblatt said they declined to comment.

Shares in the carmakers got a boost following the report, with BMW up 3.1%, Volkswagen up 2.2% and Mercedes up 1.8%.

Already struggling with a protracted slowdown in German industry and stiff competition from abroad, Germany's carmakers are battling to stem the fallout from import tariffs under U.S. President Donald Trump.

But there has been some optimism, with executives at BMW, the biggest autos exporter by volume from the U.S., and Volkswagen subsidiary Audi recently indicating there might be movement on the issue in the coming months. BMW specifically said July on when any progress might be expected.

Mercedes, meanwhile, has responded to the tariff threat with plans to add production of its GLC SUV for North America at its plant in Tuscaloosa, Alabama.