The bosses involved include Oliver Schmidt, who was in charge of VW's US environmental regulatory compliance office from 2012 until March 2015.
He was arrested on Saturday on charges that he took part in a conspiracy to defraud the US and VW customers.
Volkswagen said it could not comment on an "ongoing" legal matter.
A complaint to the US District Court for the Eastern District of Michigan, filed by the Federal Bureau of Investigation (FBI) against VW at the end of last year, accuses the carmaker of deliberately misleading regulators about cheating US pollution tests by means of so-called "defeat devices".
The complaint said Mr Schmidt and others gave a presentation to VW's executive management on or about 27 July 2015.
"In the presentation, VW employees assured VW executive management that US regulators were not aware of the defeat device," the complaint said.
"Rather than advocate for disclosure of the defeat device to US regulators, VW executive management authorised its continued concealment."
Separately, VW owners in the UK are seeking several thousand pounds in compensation over the scandal.
By the summer of 2015, the complaint from the FBI said US regulators knew that emissions from VW diesel vehicles were "substantially higher" when they were being driven on the road than when being tested.
The affidavit said Mr Schmidt - who was the general manager in charge of VW's Environmental and Engineering Office between 2012 and March 2015 - knew the discrepancy was because VW had "intentionally installed software in the diesel vehicles it sold in the US from 2009 through 2015 designed to detect and cheat US emissions tests".
In 2015, Mr Schmidt travelled to the US to talk to US regulators about the discrepancy. The filing says that during these talks, Mr Schmidt "intended to, and did, deceive and mislead US regulators" by saying the difference in the emission levels was not because of deliberate cheating.
The affidavit cites two VW employees who said that in a presentation to VW's executive management in Germany, "VW employees [including Mr Schmidt] assured VW executive management that US regulators were not aware of the defeat devices - that is the engines' ability to distinguish between the dynamometer and road mode.
"Rather than advocate for disclosure of the defeat device to US regulators, VW executive management authorised its continued concealment. "
VW said it would not be "appropriate to comment on any ongoing investigations or to discuss personnel matters".
"Volkswagen continues to cooperate with the Department of Justice as we work to resolve remaining matters in the United States," it said.
Meanwhile, in the UK, lawyers said 10,000 VW owners had already expressed an interest in suing VW. They estimated that owners could get "several thousand" pounds in compensation.
Harcus Sinclair is applying for a group litigation order - which is similar to a US class action lawsuit - in the High Court later this month.
The legal action is aimed at securing compensation for people who own or have previously owned one of the vehicles.
In the UK around 1.2 million diesel engine cars are affected by the emissions scandal.
Harcus Sinclair said it was basing its estimate of the level of compensation owners could get on the â‚¬5,000 (Â£4,300) per owner awarded in Spain and the $8-10,000 awarded in the US.
"The key allegation is that the affected cars should not have been certified as fit for sale because it is alleged that they produced higher levels of nitrogen oxide and nitrogen dioxide emissions than the rules allowed," it said in a statement.
Seventy-seven current or former VW owners have put their names to Harcus Sinclair's application for a group litigation order which will be heard in the High Court on 30 January.
The firm hopes that the marketing and publicity surrounding Monday's launch will encourage more drivers to sign up to the action.
It added it was also talking to other law firms about joining forces with them, in an effort to avoid cost duplication.
If the High Court gives the action the go-ahead, a pre-trial hearing will follow and then the trial itself in about 18 months.
In a statement, VW said: "We have been notified that Harcus Sinclair intends to bring proceedings against Volkswagen on behalf of 77 claimants in the English High Court.
"We intend to defend such claims robustly," it added.
Another law firm, Leigh Day, said it had been approached by about 10,000 VW owners regarding the emissions issue.
However, the company said it wanted to avoid the "cost risk associated with pursuing the matter through the courts".
Instead, it had submitted some test cases to the dispute resolution body, the Motor Ombudsman.
VW executives knew about emissions cheating two months before the scandal broke, but chose not to tell US regulators, according to court papers.