The club are reportedly hopeful that a new contract will be agreed to in the near future.
Crichton, 25, moved from the Rabbitohs to the Roosters at the end of the 2018 season on a three-year deal estimated to be worth around $2.2 million deal.
His contract expires at the end of the 2021 season and the Roosters want to lock him away at a cheaper price.
It comes amid interest from the St George Illawarra Dragons, who were last month linked to Crichton.
He enjoyed a great 2020 campaign as one of the best forwards in the competition and earned himself a deserved NSW origin spot where he continued his great play.
Crichton has made 96 NRL appearances since making his first-grade debut for South Sydney in 2016.
The Roosters open their 2021 campaign against Manly on Saturday, March 13 at the SCG.