The Baggies have made no secret of their desire to sign the 24-year-old defender, who has been in Gareth Southgate's England squad but has yet to win a cap.
It was thought that the centre-back's England ambitions would mean that he left for a Premier League club this summer but it seems as though he is happy to stay at the Riverside and Monk has made it clear he wants the stopper to remain in the north east.
It has been reported that Albion boss Tony Pulis will make a third bid for the player but Monk says it will make no difference as Gibson is going nowhere.
"You want to keep your most important players and the chairman (Steve Gibson) is very strong on that," he said. "We don't have to sell anyone. It's a stable club financially and it's a great place to go and work.
"We're looking to get the squad together, work hard and wait for that window to close."
And the former Leeds United and Swansea chief says he is not worried about the possibility of another bid for his star man.
"I'm not focused on that," he added. "You can never say never, but in terms of Ben's commitment to the club and the owner's idea of what's needed to be done it aligns with what I'm thinking so it's fine."