Morgan quit the Oakwell club yesterday after he refused to sign an extension to his current contact when deal did not match what he expected.
Last season, the Nationwide League Division One Play-Off finalists where keen to bring in a centre-back, and after the signing of Mike Whitlow who became 6th summer signing it was announced that no more would be signed but it now looks as though the Blades are strong favourites to make Morgan their 7th.
Neil Warnock told the official club website (www.sufc.co.uk): "We are hoping to speak to Chris and his agent but we know that we are only one of four or five clubs interested in him.
"However, he lives up the road at Penistone and maybe that could swing things our way."