According to TSN Hockey Insider Bob McKenzie, Parenteau is once again on the block.
In addition, McKenzie also reports that the Avs recently pitched Stastny a multi-year contract offer and talks are expected to resume in the near future.
Stastny, 28, is set to become an unrestricted free agent July 1. He is coming off a five-year, $33 million contract.
In 71 games with the Avs this season, Stastny registered 25 goals and 35 assists for 60 points.
His preference is to re-sign with Colorado, and he is willing to sign at a discounted rate versus what he could receive on the open market, but it's unclear how high the Avalanche is willing to go, financially.
If Stastny hits the open market July 1, several teams will be lining up for his services.
Parenteau, who is halfway through a four-year, $16 million deal, scored 14 goals and added 19 assists for 33 points in 55 games with the Avs this season.