The Australia international defender was believed to be a free agent after his original deal with the Dutch club ran out last month.
However, it now appears that a one-year extension clause has been triggered following discussions between the Eredivisie outfit and the left-back back in January.
Davidson has been linked with a move to West Bromwich Albion this summer, and it now appears that the Premier League club may have to hold talks with Heracles and pay a transfer fee if they want to sign him.
"In January, Jason and his agent indicated they would like to continue here for two (sic) more years,” the Birmingham Mail quotes Hoogma as saying.
"He wanted to wait until the World Cup with Australia to decide but because we wanted to keep him we haven't terminated his contract.
"The fact he hasn't left (by July 1) means he is under the same conditions.
“Those are the rules of the collective agreement for professional footballers and we've discussed this with Jason and his agent."