Tottenham and Manchester United have been linked with the winger.
But Howe said the new deal for the Warrington-born star had been a “reward" rather than to thwart interest from elsewhere.
Asked whether he was confident Brooks's new contract would fend off other clubs, should they try to sign him, Howe replied: “That's not even in my mind.
“The contract was to reward David and for him to kick on now and show his very best for Bournemouth for the next few years.
“The main thing for David is to keep his feet firmly on the floor, keep showing the attitude that he has, come in every day, improve and work on all aspects of his game.
“If he does those things over a sustained period of time, he will go on to have the career that he wants."
Howe added: “There are rumours about a lot of our players. For me, it was about putting him in line with some of the other players that he deserved to be (in line with).
“He has come in with a lot of potential but a lot to prove.
“In the early stages of the season I thought he was absolutely fantastic. He has developed and improved as the season has gone on and it's a reward for all those performances.
“Now he sees his future here for the long term, he can concentrate on his football and continue that path."