Everton defender Phil Jagielka
Given the lack of rivals in the running - Stoke City are next on the list at 16/1 - the development has sent Blades fans into a frenzy on social media, with the 34-year-old still held in high regard at the club he left for the Toffees a decade ago.
But how likely is a deal? HITC Sport investigates...
Is he available?
He could be soon, if Everton strengthen at centre-back as expected. However, it is unlikely they will allow him to leave until that has happened.
Despite his advancing years, Jagielka remained a regular under Ronald Koeman this past season, but with a year to run on his contract on Merseyside the Toffees perhaps would not stand in his path.
Could Sheffield United afford him?
The Blades, who are looking to strengthen in Jagielka's position, have recruited four new faces so far, at a collective cost of circa £1 million. Either they are being deliberately shrewd, or there is not a lot of money available.
However, with Kyle Walker expected to follow Harry Maguire in netting United a significant sell-on fee this summer [it is claimed they are due 10 per cent of any profit made by Tottenham on the right-back's £5 million transfer], there could be room yet for a marquee arrival.
Tottenham Hotspur's wanted man Kyle Walker
Nevertheless, Jagielka is said to earn £50,000 a week at Everton [Daily Star], and would perhaps need to take a significant pay cut to sign for Chris Wilder's men.
Wilder recently admitted his unease at signing players on significantly higher wages than others.
Would he go back to Bramall Lane?
Although not a boyhood Sheffield United supporter, having grown up across the Pennines in Manchester, the Blades are a club which Jagielka still holds close to his heart. He spent nearly decade on the Yorkshire side's books before moving to Everton and a return to the Steel City is therefore a prospect he would no doubt seriously consider.
Former Sheffield United emergency goalkeeper Phil Jagielka
Having said that, finances and Premier League football could still play significant roles in luring the England international elsewhere.
HITC's verdict: 3/10
Stranger things have happened, although a deal seems a long way off at present despite what the bookies are saying.
Could Jagielka leave Everton for Sheffield United this summer?