Hodgson was appointed in January, becoming the Hornets’ third head coach of the season, but he has been unable to steer them clear of relegation and will leave when his contract expires at the end of the campaign.
Watford have started looking at replacements and there is a desire to appoint a young, homegrown coach.
Former Hornets midfielder Eustace, who is part of Mark Warburton’s backroom staff at QPR, is admired by the Watford hierarchy and a contender for the job.
Warburton is due to leave QPR at the end of the season and it is unclear if Eustace will go with him given he still has a year on his contract.
MK Dons’ Liam Manning and Leam Richardson of Wigan are also liked by Watford, with Ipswich Town’s Kieran McKenna another on their radar.
McKenna, who was a coach at Manchester United, was only appointed by Ipswich in December, though, and is thought to be settled there.