Reported by The Mole on Wide World of Sports, it's understood the Knights' offer to King is for a new two-year deal which would see the 26-year-old remain at the club until the end of 2023.
King has been impressive this year in Adam O'Brien's side, making 13 appearances, taking him past 70 first grade appearances.
The Maitland-born Knights' junior has been with the club since his days in the 2014 and 2015 under 20s competition, before debuting in 2016.
He struggled throughout 2020 with injury, but has rebounded strongly this year, including a 45-minute effort against the Storm in a well-beaten team during Round 18. It saw King run a season-high for metres, in a performance which proved what he will be able to bring to the team, should he sign the new deal.
All Run Metres
According to the report, other clubs were showing interest in King's services from next season, however, the Knights are likely to win out.
While King isn't a starter, there is talk David Klemmer will look to exit the club at the end of the year, which may only serve to increase King's role within the Knights' middle third rotation in 2022.