"We have one (catalytic converter) in the works and we believe that will be a part of the technical solutions," Mueller told reporters at a VW event on the eve of the Detroit Auto Show.
Asked whether he expects the new catalytic converter to bring 430,000 rigged US cars into line with emissions standards, the CEO replied: "Yes, we believe that this is possible."
Mueller is meeting US Environmental Protection Agency (EPA) administrator Gina McCarthy on Wednesday, where he plans to make his proposal.
Mueller expressed optimism that VW and the EPA would be able to bridge their differences. McCarthy has previously bemoaned that both sides have failed to develop "a satisfactory way forward" despite months of talks.
"I think we can now offer a package that will come very close to what the EPA is expecting from us," the CEO said.
Part of the proposal will be an offer by the German company to repurchase some of the affected US cars, said Mueller, but declined to elaborate. Germany's Sueddeutsche Zeitung newspaper last week said VW may need to buy back around 115,000 US vehicles.
"We will offer some solutions and we will see how the reaction (from the EPA) will be," said Mueller. "We are confident that we will find a good solution."
Former Porsche CEO Mueller, who took the helm of Europe's largest automaker on September 25, said he will meet "a lot of people" in Washington on Wednesday without giving names, adding that he would also be willing to testify before US Congress on the emissions scandal, if asked.
Mueller, on his first visit to the United States since taking the top job at VW, cited differences between Germany's data protection code and comparable US rules when asked to comment on accusations by US state attorneys that VW was shielding documents from investigations.
He said VW made a "huge mistake" by cheating US emissions tests and any steps by the carmaker to overcome the crisis must include efforts to "better understand" the US market, the world's second-largest.
Asked whether he was worried about the possibility of US criminal investigations, he said: "If that was the case, then yes."