The club parted ways with Richie Wellens on Thursday after the former Rovers player had oversaw just three wins in 19 league games, leaving Doncaster second bottom of the League One table.
The recruitment process to appoint a fifth full-time manager in three and a half years is due to begin on Monday as Doncaster look for the right man to save their season.
Woodgate, who most recently managed at Bournemouth, has been made the early favourite by the bookies and is priced at 5/1 to take over at the Keepmoat Stadium.
The former Leeds United, Real Madrid, Newcastle United and Tottenham Hotspur player has also managed at his old club Middlesbrough.
Grayson, who is from Ripon in North Yorkshire, has managed in his home county before with Leeds United, Huddersfield Town and Bradford City.
He guided Leeds back into the Championship in 2010 and also oversaw the Whites' famous FA Cup win over Manchester United during his reign at Elland Road.
The 51-year-old was sacked by Fleetwood Town last month after a poor run of form but is now 6/1 to be appointed at Doncaster.
Michael Flynn, who made over 400 appearances as a player and had spells in Yorkshire with Huddersfield and Bradford, is 8/1 for the job.
In 2017 he was appointed caretaker manager at Newport County before being earning the job permanently later that year. He left the club in October after nine league matches with Newport 15th in League Two.
FC Halifax Town manager Pete Wild is also in the running at 12/1.
Next Doncaster Rovers manager odds (correct as of 8am on December 3, 2021)
Jonathan Woodgate 5/1
Simon Grayson 6/1
Michael Flynn 8/1
Neil Warnock 10/1
John O'Shea 10/1
Chris Beech 10/1
Gary McSheffrey 10/1
Graham Coughlan 10/1
Gavin Strachan 12/1
Paul Simpson 12/1
Neil Harris 12/1
Pete Wild 12/1
Aidy Boothroyd 12/1
Nigel Adkins 12/1