Paterson has been linked with the Fratton Park outfit as they seek a replacement for David Nugent, but Howe says the former Scunthorpe man is a big part of his plans and he is determined to keep him at Turf Moor.
"We are not encouraging any talks and we are not discussing any bids as far as I'm concerned and I'm sure the board are concerned," Howe told the club website.
"Martin Paterson is our player and I desperately don't want to lose him.
"I want to build my squad around our best players and I certainly think Pato is one of them."
A thigh problem forced Paterson to miss much of last season and he only mustered three goals for the Clarets.