The much-loved Blades boss Neil Warnock has been a big fan of Quinn’s for a number of years now and is set to complete the free-transfer signing following the Irishman’s release.
The Dubliner was considering a move to City to be reunited with Danny Wilson, the man who gave him his Hillsborough bow, but he is not keen on continuing playing in the second division.
Quinn is hoping to impress Ireland boss Brian Kerr and get more involvement in the international set-up after making his debut last year and he believes that he has to be playing at a first division standard at the very least.
United have been chasing a replacement for Michael Brown who left for Spurs at the turn of 2003 and Warnock has talked to Quinny about filling that role.
"United have plenty of quality players, I've spoken with Neil and there are some others in for me as well which has given me a lot of confidence," he told the Sheffield Star.
"It's important I go somewhere I can bring something to the team and also improve myself."