Losing Filppula creates a hole on Detroit's roster, one they'd like to fill with Weiss.
Weiss, 30, has spent his entire career with the Florida Panthers, but is looking to move on.
The Red Wings, Toronto Maple Leafs, Anaheim Ducks, Dallas Stars and Calgary Flames are among the teams eyeing Weiss, who had a salary cap hit of $3.1 million last season.
Weiss is believed to be looking for a five-year contract worth around $5 million per season.
If the Red Wings are unable to sign Weiss, they'll shift their focus to the likes of Mike Ribeiro, Derek Roy and Tyler Bozak.