Suter, 27, has been heavily pursued by several teams, including the Red Wings, Philadelphia Flyers, Pittsburgh Penguins and Carolina Hurricanes, while the team he's played his entire career with, the Nashville Predators, remain on the sideline in a waiting pattern.
According to various reports, the Wings originally offered Suter a 13-year, $80 million contract, then upped their proposal to $90 million.
Detroit Free Press beat reporter Helene St. James confirmed via Twitter that Wings GM Ken Holland met with Suter today, though no decision is imminent.
The Flyers have reportedly offered Suter a deal worth more than $100 million over what's believed to be a 12-year contract.
The Minnesota Wild also met with Suter today, though it's unknown what they have offered.
It's unclear if Suter will make his decision tomorrow, or wait until later in the week.