He believes the former Barnsley skipper is just the no-nonsense centre-back he needs to boost the Trotters' chances of dodging the drop.
But the lure of a return to the top flight is not enough to prise Morgan out of Bramall Lane.
And this is despite no longer being a first-team regular for Blades.
Morgan said: "I've heard about the interest from certain clubs, but until the gaffer tells me he has accepted a bid then I'll just get on with the job.
"So far, that has not happened - and, in any case, I'm happy here.
"When you get left out there is no point in moping about it. You just get your head down and work hard."