Origi spent last season on loan at Wolfsburg, where he scored just seven goals in 35 appearances across all competitions.
A Spor reports Origi's agent, Simon Bayliff, as having stated Origi will stay and fight should manager Jurgen Klopp want him to.
He said: "For me that it was a mistake for Divock to go to the Wolfsburg.
“[Jurgen] Klopp will now make a decision on him.
“If he wants him to stay, then Divock will stay or if he wants him to leave then Divock will leave.
"We are not looking to leave on loan again.
“We want to go a team that has made plans for him. In that regard, we've also spoken with Besiktas."