The former Whites midfielder, currently in charge of Oldham Athletic, is the bookies' favourite.
However, the Yorkshire Evening Post claims that no official approach has been made by the Whites, despite reports of two rounds of talks being held.
Sheridan, the current manager of Oldham Athletic, played for the Whites for seven years in the 1980s.
And according to the Sun, the 51-year-old would "jump at the chance" of a return to Elland Road, where the future of current incumbent Steve Evans looks increasingly bleak.
Despite being quoted by the Mirror this week as saying: "I'm not ready at this moment to give any answer [on Evans]. I need one or two weeks to cool down and focus better," Cellino is said to want a "quick resolution" ahead of transfer business.
Sheridan, who has never managed above League One, was only appointed at Boundary Park in January, when Oldham were five points adrift of safety, but led the Latics to the relative comfort of 17th place.
On Sunday, the Sun reported that Cellino was targeting a British manager and playing core at Leeds next season.
Fellow homegrown bosses Karl Robinson and Dougie Freedman also feature highly on the list of bookies' favourites, ahead of Italian pair Walter Zenga and Fabio Cannavaro, who've been heavily linked in recent weeks.
Evans' replacement would be the seventh manager of Cellino's two-year reign at Elland Road.