Quinn is not happy in regards to the contract offer made by Wednesday and the club have confirmed that he is looking for a new club.
Reports indicate that Paul Sturrock is to run the rule over The Blades' former Arsenal star Shaw, who is currently out of favour at Bramall Lane.
He had a loan spell at Rotherham last season before being recalled by Neil Warnock but it was pretty evident he was not part of the club's future.
Other players who have been linked are Celtic duo Ulrik Laursen and David Fernandez.