"It's still breathing and they're still in session, so anything could happen," Dayton said of the bill.
"It's a lot better than it was a week ago ... It's a lot better than it was the week before that," the governor added.
The Minnesota House and Senate have to agree on the partially public-funded stadium, or the chances the Vikings relocate to another city or are sold rise significantly.
The team's lease on the 30-year-old Metrodome expired after last season and the team is searching for a modern, long-term stadium.
The current legislative session is scheduled to end Monday, and the Republican-controlled legislature has said it won't hold a vote on the stadium until a business-tax-reduction bill and bonding bill are passed.
Republicans and Democrats, which include Dayton, are divided on the tax and bonding bills.