According to the Ottawa Sun, the two sides will resume discussions this summer.
The Avs and Stastny had started discussions on an extension in February, prior to the trade deadline, but weren't able to come to terms on an agreement.
The Sun claims Stastny, who is making $6.6 million this season, could earn between $6.5 million to $7 million on the open market as a free agent.
It's believed the Nashville Predators will go after Stastny on the open market, if he remains unsigned by July.
Several teams will be in the market for a top center, including the Toronto Maple Leafs, Winnipeg Jets and Buffalo Sabres.