Trippier rejoined Newcastle late after playing for England at the European Championship and did not feature in the 1-0 Premier League victory over Southampton on Saturday.
"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 told reporters on Friday.
"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. (He's) a valuable member of the squad. His professionalism has been first class."
Trippier, who played six of England's seven games at Euro 2024, has been linked to Everton, where he would reunite with manager Sean Dyche they spent three years at Burnley together.
"I'm not really sure where this has come from. He's preparing as we all are for the game on Saturday," 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. Bournemouth kicked off their campaign with a 1-1 draw at Nottingham Forest.
