Petratos has missed Ulsan's past four matches and hasn't appeared since starting against Brisbane in the AFC Champions League (ACL) on May 10.
The 24-year-old signed a three-year contract with Newcastle in January but Ulsan hijacked the move in February by paying Roar a transfer fee for his services, with the Jets receiving compensation.
Roar midfielder Dimitri Petratos netted one of the all-time great Hyundai A-League goals on Friday night.
The Jets told Goal: "The club is interested in signing Dimitri Petratos given his latest contractual developments with Ulsan."
It has been speculated Brisbane and Sydney FC could also be interested in signing Petratos.
Since joining Ulsan, Petratos has made nine appearances in the club's 22 matches in all competitions.
Petratos' younger brother Kosta has signed a one-year contract with Newcastle after spending the last two seasons with Perth Glory.
Having played for both Roar and Sydney in the A-League, Dimitri has made 124 A-League appearances and scored 19 goals.