The 33-year-old England international was an unused substitute in the Magpies’ 1-0 win against Southampton on Saturday.
Howe said Trippier “continues to be really valued” by the club.
“The situation is business as usual, Tripps has trained really well this week. I’m surprised by a lot of the stories that have come out,” Howe said in a news conference on Friday.
“[He’s] a valuable member of the squad. His professionalism has been first class.”
Trippier, who joined the club from Atletico Madrid in 2022, is behind Tino Livramento in the pecking order for the right-back position.
He has been linked with a move to Everton to reunite with Sean Dyche, who managed him for three years at Burnley.
“He’s trained really well since he came back from the Euros – I think he’s only had two weeks of training, hence the reason why he didn’t start last week,” Howe added.
“I’m not really sure where this has come from. He’s preparing as we all are for the game on Saturday.”
Newcastle blocked Trippier from leaving the club in January following interest from Bayern Munich and Saudi Arabia.
Howe added: “His leadership skills, his ability with the ball, his assist record, everything he brings to the group we definitely want here.”
Newcastle travel to Bournemouth on Sunday for their second Premier League match of the season.