The 28-year-old had made just one start prior to the 2013 season, but was promoted to starter for the Cleveland Browns in the third week of the campaign, leading the team to a three-game winning streak before sustaining a season-ending knee injury.
The retired quarterback, who now works as a pundit, told the team's website: "You look at that first game against Minnesota and how he brought them back there at the end, he just showed great poise and confidence, and I think the team really responded.
"It says a lot about how a team really responds and rallies around a guy. I think he's a guy that really merits some strong consideration.
"If you look around the [AFC North], Pittsburgh's got [Ben] Roethlisberger, Baltimore's got [Joe] Flacco, and of course, Cincinnati's got [Andy] Dalton. Cleveland's got to find a quarterback."
Hoyer will remain with the Browns for the 2014 season, having signed a two-year contract with the side in May.