Quinn had been linked to a number of vacancies in the NFL, but has been unable to meet with all of the teams while the NFC West champions have made their way to the Super Bowl.
The 43-year-old told NBC Sports: "I had a good visit with [Cleveland] and a lot of respect certainly for their organisation and Joe Banner and Jimmy Haslam. I also had a good visit with the guys at Minnesota and both of those guys have hired some great coaches.
"It was a great experience to go through and even more importantly having the support of John Schneider and Pete Carroll to have a chance to be so supportive of that. I couldn't be more fired up to be a part of this and moving forward here keeping the focus on our team, which it is."
The Seahawks will face the Denver Broncos in the Super Bowl next weekend.