Matt Burton has played three State of Origin matches for NSW and made five Test appearances for Australia, including the Kangaroos' 2022 World Cup campaign in England.
The Canterbury-Bankstown centre can speak with rival clubs from November 1 about a contract beginning in 2028, as his current deal expires after 2027.
9News reports Burton's management has emailed NRL clubs about his availability, with the player set to consider offers from November.
The Bulldogs remain keen to retain him, but their changing halves combination leaves uncertainty over his role.
Lachlan Galvin established himself in the halves this year, captain Stephen Crichton has emerged as another five-eighth option, and prospect Mitchell Woods continues to develop.
Burton shifted to centre in the second half of the season, returning to the position where he won the 2021 premiership with Penrith.
He has shown his ability at both five-eighth and centre, while his acceleration and powerful left-footed bombs could appeal to clubs seeking attacking threat.
Canterbury is likely to view him as a long-term outside back, but Burton will compare offers before deciding his next move.