The Free Press claims the Wings are mulling over the idea internally, and assistant coach Tom Renney, who coached Redden in 2008-09, will factor into the club's decision.
Redden signed a six-year, $39 million contract with the Rangers in 2008, but has spent the last two seasons in the AHL
The Red Wings are one of several NHL clubs looking to add depth to their blueline and will have some competition for Redden's services.
Redden's agent, Don Meehan, did not confirm or deny having preliminary discussions with other teams about his client.
"I'm not permitted to talk to anyone about Redden nor can they initiate contact with me (until he becomes a free agent)," Meehan told TFP.
With roughly $9 million in available salary cap space, the Wings have enough room to sign Redden to a small contract and still look to make other significant upgrades to the roster throughout the season.
If the Wings are unable to sign Redden, however, GM Ken Holland will continue to explore options on the trade front.
Holland has been involved in several trade discussions with some of his counterparts over the last few days.
In 994 NHL regular-season games, Redden, a two-time NHL All-Star, has accumulated 106 goals and 344 assists for 450 points.