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 FRANKFURT — Volkswagen is expected to offer cash to the owners of diesel cars in the United States this coming week as it steps up an effort to recover some of the good will it lost after admitting in September that the vehicles were programmed to cheat on emissions tests. 
 
 Volkswagen officials said the company would make an announcement on Monday but would not confirm a report on an automotive website that diesel owners would be offered up to $1,250. The site, The Truth About Cars, said the owners would get a cash card worth $500 that they could spend any way they liked, and another $500 to $750 that they could spend at a Volkswagen dealer. 
 
 The company faces lawsuits from owners seeking compensation for the decreased resale value of the roughly 500,000 Volkswagen and Audi vehicles that were equipped with illegal software. It was not clear whether owners would have to give up any rights to sue if they accepted the cash. 
 
 The software allowed the cars to detect when emissions testing was underway and turn on the emissions controls. But when the cars were on the road, they emitted up to 40 times the permissible amount of nitrogen oxide, which is harmful to the lungs. 
 
 Volkswagen has promised to make changes to cars so they comply with emissions limits. But the repairs are likely to be costly and complicated, and Volkswagen has not said how they would be carried out. Two dealers said on Saturday that they were aware that Volkswagen was planning something but did not know specifics. “There is a program in the works with VW, that I do understand,” said Alan Brown, head of an association of Volkswagen dealers. 
 
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 Cars with illegal software include diesel Golf, Jetta, Beetle and Passat models sold since the 2009 model year, as well as Audi A3 cars. 
 
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 The Environmental Protection Agency said on Monday that some larger Volkswagen, Audi and Porsche diesel vehicles, all of which are produced by Volkswagen, also had software that was not allowed. 
 
 But Volkswagen has denied that the software in those cars was designed to cheat on emissions tests, and they would probably not be eligible for the cash compensation. 
 
 Already, Volkswagen has been trying to minimize the damage to sales by offering cash incentives to existing owners if they buy or lease a new car, as well as big discounts for all buyers. ||||| Update: Added background. 
 
 Volkswagen of America, in a bid to regain the trust of current diesel owners, will announce a prepaid card campaign on November 9, TTAC has learned. 
 
 The program, detailed to dealers Thursday in preparation of its public announcement, is aimed at current owners of affected TDI models regardless of whether they bought their car new or used. 
 
 Two prepaid cards will be offered to those TDI owners. The first one will be for $500 and has no restrictions on where it can be used. The second, which may be valued between $500 and $750, will be limited to use at Volkswagen dealerships. 
 
 According to our tipster, owners of affected models will need to visit their local Volkswagen dealership with proof of vehicle ownership to activate the prepaid cards. 
 
 Owners can find out if they qualify for the “TDI Goodwill Program” by going to www.vwdieselinfo.com and doing a VIN lookup on or after November 9. If they qualify, owners will then be asked to register to receive updates regarding future developments on their diesel vehicles. 
 
 The program is expected to apply only to four-cylinder diesels for now, though it could be expanded to 3-liter V-6 diesels later. 
 
 Representatives for Volkswagen of America could not be reached for comment. 
 
 The additional cash could be a plus for those looking to stay with the brand but get away from their diesel cars. Volkswagen announced October 31 that they would subsidize dealers to take in TDI vehicles on trade at pre-crisis valuations, on top of a $2,000 TDI owner loyalty discount announced October 2.
– Volkswagen might be looking to buy its way out of the public relations disaster that keeps on giving: According to a report on The Truth About Cars, the German automaker will offer owners of affected diesel cars up to $1,250 in cash under a "TDI Goodwill Program" set to roll out Monday. That would come in the form of a $500 prepaid gift card and $500 to $700 to be spent at Volkswagen dealerships; VW would only confirm that an announcement is coming Monday, reports the New York Times. "There is a program in the works with VW, that I do understand," says the head of a dealership association who was not briefed on specifics. What's not clear: Whether owners of affected cars who are involved in class-action lawsuits against VW would have to abandon those claims.