The Blades are leading the hunt for his signature on a Bosman but are in no rush to push the deal through.
Liddell is one of three players being chased by the Yorkshire outfit who finished a place behind Latics in the First Division last season.
Clarke Carlisle at QPR and Sheffield Wednesday's Wayne Quinn are the others, but like Liddell, will have to wait for their move to Bramall Lane.
Blades boss Neil Warnock said: "We have spoken to the agents for Liddell, Carlisle and Quinn, plus others, and heard encouraging things.
"But nothing definite will happen until mid-June."
After saying his farewells at Latics earlier this month, Liddell expressed his desire to sort his future out quickly.
He was hoping to have an agreement in place before him and some of the Wigan players jetted off for a short break in Spain last week.
Preston and Bristol City – hoping for a First Division return through Sunday's play-off final – are also in the hunt for Liddell.
But the Blades are his preferred option with Sheffield only a short distance from his Leeds home.
The futures of the other Latics players coming towards the end of their current deals should become clearer this week and next.
Six are mulling over fresh one-year deals and will be ready to give their answers to manager Paul Jewell soon.
Skipper Jason de Vos told the Evening Post last week that he would make a decision by Thursday.
He then joins up with the Canada squad for a summer of international football.
Vice-captain Matt Jackson has indicated he is content with the terms on the table, while the others offered deals are Mike Flynn, Paul Mitchell and goalkeepers Gary Walsh and James Salisbury.
Meanwhile, two former Latics goalkeepers had contrasting fortunes in cup finals at the weekend.
Roy Carroll picked up a winners medal at the Millennium Stadium as Manchester United beat Millwall 3-0 in the FA Cup Final.
The Northern Ireland international was an 83rd minute substitute for the almost redundant Tim Howard.
In Scotland, Derek Stillie had to be content with a losers medal as Dunfermline were beaten 3-1 by Celtic at Hampden Park.
It was Stillie's last game for the Pars having turned down a new contract and he could be set for a move to the Continent.
* Former Latics midfielder Darren Sheridan has been released by Oldham after three years at Boundary Park.
Source: Wigan Evening Post.