Though the pass-rusher can now enter the free-agent market, the Vikings believe Griffen will return to Minnesota.
"Everson's a terrific person for us. I think our situation is the right one for him and we expect him to be back," head coach Mike Zimmer said, according to NFL.com's Nick Shook.
Griffen was set to count for $12.9 million against the cap next season before he declined his option. The Vikings now have a league-low $1.4 million worth of cap space for 2020, according to Over the Cap.
It will require some financial gymnastics to get Griffen - who has put up 57 sacks since 2014 - back under contract, but Zimmer believes the Vikings will find a way.
"I think he wants to be back, so, you know, those kinds of things usually work its way out," he said.