New Hammers manager David Moyes is a huge fan of the hard-working Cherries man and has made him a key target for January.
The West Ham manager believes the squad he inherited from Slaven Bilic is weak in central midfield, and is looking to bring reinforcements.
However, Howe has told West Ham to forget about making a move.
Ahead of the Boxing Day clash with the Hammers, Howe said: “Harry is going nowhere.
“He is integral to the team, we gave him a four-year contract, demonstrating our love for him. He is so important for us.
“Harry is a leader. I would not say he is a shouter and screamer. He is a leader with his endeavour and passion which comes out in the match."