The 26-year-old Irishman, who has enjoyed arguably his best season for the Blades, still has 12 months left to run on the three-year contract he signed in 2010.
When asked if would still be at Bramall Lane next season, Quinn said: "I hope so yes. I haven't had any thoughts about my future, I'm just trying to deal with this defeat and we'll look at it in the summer."
He added: "The lads have been brilliant all season. I'm proud to say they're my team-mates and walk out on to the pitch side by side with them. It's probably been the most enjoyable season of my career and I just want to thank them.
"We've grown as a squad. No-one has ever buried their heads in the sand during all the trials and tribulations and that's why we'll come out stronger for next season.
"I love this club. I've tried my best for the fans and I'm devastated for them after the support they've shown all season, it's been incredible and I'd like to thank them as well. We'll go again next season because it's a massive club and needs to be back where it belongs."