Speaking to the Sunday Mercury, Gunnarsson said: "I've read that some big clubs might be coming in for me in the summer but I'm not thinking about that. I want to stay at Coventry.
"It's not all about the money. I can learn a lot here, develop as a player, but if I went to a bigger team I would probably be on the bench most of the time.
"I didn't expect to play as many games this season and the gaffer didn't expect me to either, but I've done well so he's kept me in the team and that's been great for me.
"I've worked hard to get here but I'm not going to stop and think, 'that's enough'.
''I want to go higher and get higher with Coventry - I can't wait for next season when we can progress as a team."