A framework deal to buy back nearly half a million 2.0-liter diesel vehicles equipped with cheating devices has been reached between Volkswagen AG and U.S. officials.

According to Reuters, this settlement still in process of the so-called Dieselgate scandal revealed last September would include TDI versions of the VW Jetta, Golf, and Audi A3. Not included are larger 3.0-liter diesels which also may emit over-the-limit levels of pollution, including nitrogen oxides.

The German automaker is expected to say as much to a federal judge in San Francisco tomorrow.

No comment was offered to Reuters by VW, the U.S. EPA, or the Justice Department.

VW has also agreed to pay a compensation fund to owners, with the amount each owner might receive not yet specified, according to Reuters which cited an un-named source.

This fund could top $1 billion, according to an un-named source speaking to Reuters.

The time for owners to decide whether they wish to sell back their cars is reportedly two years. Whether VW may then recoup losses by reselling the vehicles is not clear at this time.

In a separate report, Die Welt newspaper in Germany reported VW has in the settlement agreed to pay each affected diesel owner $5,000.

Volkswagen may also according to the report offer to repair affected vehicles if U.S. regulators approve the fix, Currently it is not clear if these will even be deemed fixable by the U.S. EPA.