The 25-year-old has impressed for the Blades in League One this season. The club rejected several bids for the midfielder during the summer transfer window.
“We’ve done well to keep so many of the lads on board and it looks like the club are giving it a really good go to get back into the Championship this year,” Quinn told Sky Sports.
“That is refreshing and as much as I want to play in the Championship and beyond I am happy to get my head down here and help them get back there as soon as possible.
“I’ve worked with the gaffer before when I went on loan to MK Dons and his philosophy and attitude towards the game makes it such an enjoyable place to be at.
“The lads have taken to it really well, so if the lads are still pushing for promotion when January comes round then I don’t see any reason for me to leave.
“Sheffield United is a massive club and there is so much potential for us here not just to get back into the Championship, but maybe even get back-to-back promotions because others have done in it.
“That is the ambition and I’m delighted to be a part of that, so we will just have to wait and see what happens over the coming months I guess.”
