The Englishman, who has guided the Cherries from League Two to the Premier League during his two spells in charge, has been touted as a target for both Arsenal and Everton.
According to The Mirror, Bournemouth are convinced that Howe will remain at the helm, even if a bigger club comes calling.
"I don't think he will be looking at a top-10 finish to move on. I think it will be a top-10 finish for the club to move on," Cherries defender Steve Cook is quoted as saying.
"I feel we can do that. We still have nine games left. We are still on the edge, so we need a couple more wins to feel safe."
Bournemouth sit in 12th place in the league ahead of this weekend's home match against Tottenham Hotspur.