The final year of Suh's rookie contract with the Detroit Lionsvoided on Friday. Team president Tom Lewandsaid earlier this month that he believes there is a "very, very good chance that we can get something done with him in the next few weeks."
Cole said that Suh "would love to be with the Seattle Seahawks. This is his No. 1 choice." Cole added that "because Suh is from the Northwest area, grew up in Portland, he'd like to be there."
Teams can enter negotiations with representatives of players on March 7 and sign players to contracts starting at 4 p.m. ET on March 10.
It could be difficult for Seattle to sign Suh because the team is expected to try to sign multiple key players to contract extensions, including quarterback Russell Wilson.
In January, Lions general manager Martin Mayhew said he's not ruling out the possibility of using the $26.9 million franchise tag on Suh.
The Lions selected Suh with the No. 2 overall pick in the 2010 draft. The 28-year-old has earned four Pro Bowl nods and been selected to four All-Pro teams. Over 16 games this season, Suh recorded 54 tackles and 8.5 sacks while helping the Lions rank first in the NFL in rushing defense.
ESPN's Adam Schefter reported in September that Suh is likely to leave Detroit in free agency, but Mayhew reportedly said Suh is "open" to remaining with the Lions.
The Lions went 11-5 and finished in second place in the NFC North this season before falling to the Dallas Cowboys in the Wild-Card round of the playoffs.