Davidson, 23, had been linked with a move to join countryman Adam Taggart at Fulham after playing in all three of the Socceroos group games at the 2014 FIFA World Cup in Brazil.
Eredivisie side Heracles contended it had opted to trigger an automatic extension to the left-back's contract for at least a further season, having been given an expression of the player's desire to remain in the Netherlands by his agent in January.
However, Davidson's Polman Stadion future now looks to be in doubt, with Heracles chairman Jan Smit quoted as saying this week: "Because he has not reported on Monday, Jason has not fulfilled his obligations.
"From what I understand, he is in England looking for a new club. Maybe that offers a solution."