McGregor is out of favour at Ibrox despite and despite the departure of Rangers manager Alex McLeish is looking for new opportunities away from Glasgow for the 24 year old to find a first team spot.
The keeper revealed: "I want to keep playing first-team football and if that does not happen at Rangers then I'll need to see about looking elsewhere.
"It is flattering to be linked with a club such as them (Sheffield United). I did not expect that." Other clubs, mainly from Scotland are also interested.
Meanwhile Sheffield United should make former Everton defender Li Tie their first summer signing. Reports from China suggest that Tie, 28 is only a 'fine print' away from completing a deal.
"Both sides are very positive," the Beijing Times quoted Li as saying. "There are only a few remaining details to be discussed. Barring any surprises, we should be able to settle this by the start of next month."
Tie joined the Evertonians in August 2003 and previous enjoying a successful seasons long loan from Chinese based Liaoning Fushen but after a season plagued by injuries the Chinese international (79 caps - 5 goals) was released from Goodison Park on Monday (8 May).
During his time at the Premiership outfit he played 36 (+ 4 as sub) whilst failing to hit the back out the net during the four years spell. His signature, should it occur is expected to happen after the 2006 World Cup in Germany.