As the Vikings' designated franchise player, Greenway was tendered a one-year guaranteed contract that pays him 120 percent of last year's salary or the average of the top five highest-paid linebackers ($10 million), whichever is higher.
Greenway was excited when the team placed the franchise tag on him last month.
The NFL Players Association has rejected the use of the franchise tag, and it remains to be seen whether or not it will be a part of the next collective bargaining agreement.
The current CBA expires Thursday night.
Greenway, who led the team with 144 tackles last season, is seen by the Vikings as a centerpiece of a defense that's facing offseason changes.
The five-year NFL veteran has started 62 of the 64 games in which he has played since the Vikings selected him in the first round of the 2006 NFL Draft.
The Associated Press contributed to this report.