In a reply to a fan question on Twitter, King wrote he believes Bell will become a free agent and sign with the highest bidder.
He added that the Oakland Raiders will be a team to watch if the running back becomes available.
Bell played under the franchise tag in 2017 but said at the end of the regular season he would consider sitting out 2018 or retiring if he gets tagged again.
According to ESPN.com's Jeremy Fowler, Bell added, "Just get the numbers straight, exactly where we want them. I'm not going to settle for anything. I know what I do and what I bring to the table. I'm not going out here getting the ball 400 times if I'm not getting what I feel I'm valued at."
In five NFL seasons, the 25-year-old Bell has been named to the Pro Bowl on three occasions, and he is a two-time First Team All-Pro selection.
The 2017 campaign was one of Bell's best, as he rushed for 1,291 yards and nine touchdowns on an NFL-leading 321 carries to go with 85 receptions for 655 yards and two more scores.
Although the Jacksonville Jaguars upset the Steelers in the AFC Divisional Round, Bell was a driving force behind Pittsburgh's dynamic offense along with quarterback Ben Roethlisberger and wide receiver Antonio Brown.
The Raiders took a huge step back offensively and as a whole in 2017, as they fell to 6-10 after making the playoffs at 12-4 in 2016.
That led to Jack Del Rio's firing and Jon Gruden's return as head coach.
Although Oakland brought running back Marshawn Lynch out of retirement, it ranked just 20th in the league in rushing.
Lynch ran for 891 yards, calling into question whether he's still a bell-cow back.
Bell's precisely that, and he would provide a huge boost to the Raiders or any other team that signs him.