Sheridan, 51, had been available at 12-1 when the firm opened betting this weekend but the former Whites midfielder was a 1-6 favourite on Monday evening, having been slashed into 6-4 earlier in the day.
The Latics boss, who has also managed Chesterfield, Plymouth Argyle and Newport County, enjoyed seven years at Leeds as a player between 1982 and 1989.
Sheridan is currently in his second spell in charge of Oldham having guided the club to the League One play-offs in 2006-07 when the Latics finished sixth.
Oldham - still in League One - have finished this season 17th.
Steve Evans remains head coach of United but chairman Massimo Cellino has yet to offer him an extension to his contract which expires on June 30.
Evans had still been 3-1 second favourite with Sky Bet to be head coach on the first league game of next season but the Glaswegian has now drifted out to third choice at 10-1.
Italy’s World Cup 1990 goalkeeper and short-lived Sampdoria boss Zenga had been odds-on favourite for the post at 4-6 but the 56-year-old is now 16-1.
Former Italian World Cup winner Fabio Cannavaro is second favourite at 8-1, with ex-Crystal Palace, Bolton Wanderers and Nottingham Forest boss Dougie Freedman 16-1, along with Zenga and Gus Poyet.
David Moyes and Nigel Pearson are both 20-1 with Steve McClaren, Paul Clement and Steve Bruce all 25s.
Other new additions to the Sky Bet market on Monday were former Inter Milan boss Walter Mazzarri and ex-Milan manager Sinisa Mihalovic who are 40-1 and 33-1 respectively.
Zenga, though, is clearly the most bizarre name on the list.
The Italian made 58 appearances for the Italian national side and enjoyed 17 years at Inter Milan where he made 328 appearances between 1978 and 1994.
The former shotstopper has managed 16 different clubs since pursuing a coaching career in 1998, most notably Sampdoria who sacked the Italian after only 14 games in charge last year.
Zenga, who initially pursued an acting career after retiring, became player-manager of American club New England Revolution for a year in 1999 before a short stint in charge of Italian Serie D team Brera Calcio.
In 2002, Zenga then moved to Romania - the country to which he now holds citizenship - and went on to manage Naţional Bucureşti, Steaua Bucureşti and Red Star Belgrade - each for no longer than a year.
At Steaua, Zenga won the domestic title and reached the last 16 of the 2004-05 UEFA Cup after eliminating Valencia.
The former goalkeeper then led Serbian team Crvena Zvezda to a domestic double in 2005-06 and has been in charge of another 10 clubs in ten years since, including Sampdoria in 2015.
The other club’s on Zenga’s CV are Turkish side Gaziantepspor, another Romanian side in Dinamo Bucureşti, Italian clubs Catania and Palermo, Saudi Arabian side Al-Nassr and UAE clubs Al-Ain, Al-Nasr, Al Jazira and Al-Shaab.
Sky Bet next Leeds United head coach betting (at 6pm on Monday, May 9): John Sheridan 1/6, Fabio Cannavaro 8/1, Steve Evans 10/1, Simon Grayson 16/1, Dougie Freedman 16/1, Walter Zenga 16/1, Gus Poyet 16/1, David Moyes 20/1, Nigel Pearson 20/1, Steve McClaren 25/1, Paul Clement 25/1, Steve Bruce 25/1, Sinisa Mihajlovic 33/1, Michael Appleton 33/1, Chris Coleman 33/1, Roberto Di Matteo 33/1, Dennis Wise 40/1, David O’Leary 40/1, Walter Mazzarri 40/1, Brendan Rodgers 40/1, Roberto Mancini 40/1, Alan Smith 40/1.