Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
United have held initial talks about a possible deal to bring the 31-year-old Senegal international to Elland Road.
News of Leeds manager Neil Warnock's interest comes as something of a surprise considering the history between the pair following an incident during Warnock's spell in charge at QPR.
Warnock labelled Diouf a 'sewer rat' after accusing the striker of abusing Jamie Mackie while he lay on the pitch with a broken leg during Rangers' FA Cup clash with Blackburn last January.
However, Diouf insists there is no problem between himself and Warnock and that he would be thrilled at the prospect of joining Leeds.
"I know people have talked about the incident between me and Neil Warnock but it is in the past and is not an issue," Diouf told Sky Sports News.
"I have the utmost respect for Neil Warnock and I'd be delighted to help Leeds gain promotion to the Premier League."