Code Sports reports the Roosters have asked Sam Walker's management for a decision by next Monday, and the halfback is willing to respond.
Walker has told his agent, Clinton Schifcofske, that he would rather remain with the Roosters than enter free agency, the publication reports.
He is currently earning about $1.05 million and has been offered a new deal that would add $350,000 to his annual pay.
Walker's contract has been a major NRL talking point since he helped the Tricolours beat Newcastle in the grand final.
He had been expected to wait until after the Rugby League World Cup, reach the November 1 free-agency date and test his market value.
Although the PNG Chiefs' interest had worried Roosters supporters, current indications point to Walker staying and forming a halves partnership with Hugo Savala.