It was reported in the local press in the north east that Rafa Benitez was set to try and prize Wilson away when the transfer market opens.
Reports claimed that sources in Hampshire had suggested a move was on the cards, but Howe has dismissed it as spurious and told his players to ignore all speculation.
He told the Echo: “It’s got no relevance to us. Not to the football club or to Callum. There’s no substance to the story.
“The only time that will influence him is if he believes it or reads it himself. And I would encourage my players to just concentrate on their day-to-day job.”
Middlesbrough climbed into the Sky Bet Championship play-off positions as Patrick Bamford's first career hat-trick secured a comfortable 3-0 win over Leeds.
Louis Longridge and Greg Docherty will leave friendship at the side of the pitch for 90 minutes on Sunday when Falkirk face Rangers at Ibrox.