The English international will remain with the Bunnies until at least the end of the 2019 season despite drawing interest from the Eels on a multi-year contract.
Burgess told Parramatta on Tuesday of his desire to remain in South Sydney, despite not having a deal in place beyond this season.
The 26-year old is confident of earning a new contract under super coach Wayne Bennett after appearing in 27 games for the Rabbitohs last season.
Burgess was reportedly close to agreeing to a deal with the Eels but it ultimately fell through.
“He will be with us in 2019 and Wayne has always indicated he wants him here,” Richardson told NRL.com.