Graham,who has played 185 matches in the NRL with the Bulldogs and Dragons,will be the next piece of a major roster reshuffle at the Dragons.
The 34-year-old,who is in the final year of his NRL deal,has been under increasing scrutiny during the Dragons'run of poor performances.
The club said they've been in discussions with Graham and his management about a return to the United Kingdom,which could be with"immediate effect".
"The Dragons will consider this option for Graham on the merit a replacement player is secured by the club prior to his release,"St George Illawarra said in a statement on Thursday.
It is expected Graham will link with his boyhood club St Helens,having debuted for them way back in 2003.
The English giant has a vacancy to fill on their roster after releasing Luke Thompson to join the Bulldogs last week.
Thompson is currently serving a two week quarantine period in a Melbourne hotel before being available for selection.
Graham chalked up the remarkable 400 top grade game milestone across both the Super League and NRL last year,but has been part of a team struggling team in 2020.
The Dragons lifted themselves off the bottom of the ladder when they.
this week and Graham could be the next experienced player to head for the exit at the joint venture.
Asked about Graham's performance against the Sharks,Dragons coach Paul McGregor said:"I thought his game last week[against the Bulldogs] was fine. His last two games have been good."
The England international has been named part of McGregor's starting side for the clash against the Titans in Brisbane on Saturday.
Get our Morning&Evening Edition newsletters