Thompson will play his first game of the season this weekend after completing an excruciatingly long recovery from a foot injury.
The powerful English prop has been heavily linked with a return home to the English Super League, but may ultimately contemplate another year in the NRL and a chance to reach his potential in the competition.
Thompson arrived at Belmore during 2020 amidst coronavirus lockdowns and quickly became one of the club's most important players, but has struggled to say on the field since, playing 15 games in 2021, 13 in 2022 and none so far this year.
Despite that, News Corp is reporting a three-club race has broken out for his services, with the Bulldogs reportedly interested in retaining Thompson alongside the Wests Tigers and St George Illawarra Dragons.
The Tigers are the latest club to join the race, with the report suggesting the club will hold meetings with the experienced 28-year-old forward's management this week.
The Dragons have been interested in Thompson for some weeks now if reports have been believed, with incoming coach Shane Flanagan looking for a rapid rebuild at the Red V.
The club has given a number of players permission to exit at the end of the season, opening up roster spots for a potential play at Thompson. The Dragons have also reportedly shown interest in Tino Fa'asuamaleaui for next year, and Payne Haas for 2025.
Despite all that, Canterbury director of football Phil Gould has previously not ruled out retaining Thompson, and the Bulldogs could make a play with one of their few remaining roster spots for 2024.
If they do, Thompson's presence could prove valuable to the side who continue to look at their long-term rebuild under Cameron Ciraldo in 2024.