It was claimed by the Daily Mail last week that the Blades, along with Brighton and Burnley, were considering a move for the 25-year-old.
However, as reported by 90min, that story has since developed. A summer deal is slightly complicated but not entirely impossible.
Hendry is on loan at Belgian club KV Oostende, who have an option to buy the Scotland international at the end of the season for around £2million.
Effectively, Oostende can then sell for a quick profit with £10m the rumoured asking price – money Celtic would not see.
It is claimed Aston Villa, Brighton and Wolves are keen while Newcastle, Leicester, West Ham and Crystal Palace have also kept tabs on his progress.
Oostende are fully aware of the emerging interest. In an ideal world, they would prefer to keep him but are open to the idea of cashing in immediately.
Blades boss Chris Wilder has had to contend with a number of key defensive injuries this season, so the need for cover is apparent.
Whether the club’s recruitment team can be tempted into meeting the potential price tag of Hendry, remains to be seen.
Here are the latest transfer headlines from Sheffield United and their Premier League rivals: