McCarthy is scheduled to meet with Volkswagen Chief Executive Officer Matthias Mueller at his request on January 13 in Washington - the day before the California Air Resources Board is scheduled to publicly respond to VW's proposed repairs.
CEO Matthias Mueller will visit the Detroit auto show next week.
Volkswagen AG may buy back tens of thousands of cars with diesel engines that can't be easily fixed to comply with USA emissions standards as part of its efforts to satisfy the demands of regulators, according to two people familiar with the matter.
The EPA said this week that after months of talks "recall discussions with the company have not produced an acceptable way forward".
VW declined to comment on the impending meeting. Nevertheless, VW's brand chief Herbert Diess recently revealed his confidence that a solution with the EPA would be reached shortly.
In an interview with Reuters, Diess said fixing older VW cars equipped with 2.0-liter diesel engines will be more hard than bringing more recent models into compliance.
The Wolfsburg-based company has to choose from a number of solutions, such as refunding the purchase price of about a fifth of the 580,000 diesel cars affected or offering a new one at a significant discount.
Two U.S. senators, Edward Markey of MA and Richard Blumenthal of CT, on Thursday called on VW to offer buybacks and also "guarantee owners a speedy fix that minimizes their hassle, and full compensation for the loss of resale value and lost fuel economy".
Mueller was named CEO in September - days after longtime CEO Martin Winterkorn resigned.
Also, in 2014, Hyundai and Kia paid $100 million to the US, for violating the same environmental act. The vehicles then switch off those measures in real-world driving conditions, spewing harmful gases at up to 40 times what is allowed under federal environmental standards.
The lawsuit could result in a fine of US$20 billion or more on VW.