Championship sides Aston Villa, Wolverhampton Wanderers and Derby County have also submitted bids, along with at least one more Premier League club.
Mooy's parent club, Manchester City however, may be reluctant to release him for under £10 million ($17.3 million).
Sparked by a dazzling season on loan at Premier League-promotion hopefuls Huddersfield, the bids have left City coach Pep Guardiola with a conundrum.
Does he cash in on a player who cost City just a few hundred thousand Australian dollars from feeder club Melbourne City, or does he bring the 26-year-old into the inner sanctum at the Etihad next season?
Surprisingly, Huddersfield - the team which have benefited immensely from their Player of the Year's mastery - have yet to register their interest in keeping him beyond this season.
Mooy is contracted to City until 2020, on a deal said to be worth around $4 million a year.
While Guardiola ponders the possibilities, Mooy's agent Paddy Dominguez is on his way to the UK to "discuss the options for next season".
Mooy's value could spiral even higher if he can help the Terriers overcome Yorkshire rivals Sheffield Wednesday in Thursday's (AEST) second leg of their Championship play-off.
The winner will face either Reading or Fulham in the play-off final at Wembley on May 30, in the match dubbed the richest in football.
Guardiola watched the first leg, and was said to have been impressed by the way Mooy controlled the midfield during the 0-0 draw at the John Smith's Stadium.
While Dominguez would not be drawn on what he described as "speculation" over Mooy's future, he did confirm that the Terriers were not, as yet, one of the bidders.
"I've had no contact from anybody at Huddersfield regarding Aaron Mooy for next season," he revealed.
"That doesn't mean they won't contact me ... it just means they haven't to date."
Asked what the options might be for Mooy, Dominguez added: "The options are whether he stays at Manchester City, or whether Huddersfield want him should they be promoted, or there is the possibility of a sale to other clubs."