The 21-year-old has scored six times this season ahead of tomorrow’s Championship game with Brentford.
Premier League Fulham and Cardiff City are reportedly interested in the £5m-rated talent to bolster their hopes of avoiding an immediate relegation.
He netted twice in the 3-2 win at QPR a fortnight ago and his general form has helped aid the Tigers’ own push for safety, which has seen just one defeat in the last seven outings.
Asked if there had been any approaches for Hull’s reigning supporters’ and players’ player of the year, Adkins said: “None. I’ve just been speaking to a colleague and he said, ‘You’ll probably get asked some questions about Jarrod.’
“But I’ve not seen it (reports). I’ve just been made aware of it.
“We talked about it weeks ago and Jarrod will get linked. As it stands we’ve not had any bids for Jarrod. He’s doing really well for us and we want that to continue.
“If there’s speculation it means he’s doing well. That’s very good for us.”
Adkins maintained he is not worried the player, who joined from Hereford in 2014, will depart, and added: “We’re not looking for him to leave.
“He’s just got to keep playing and working hard. January will be January; the question will get asked all the way through, but as far as I’m aware we’ve not had any bids for him.”
Bowen’s long-term development could be better served at the Tigers, believes Adkins.
Hull’s boss said: “Young players need to play. You look at some who have jumped and gone for the money somewhere else and they’re not playing. He’s a young lad, so just go and play football.
“It’s been quite challenging for him this season, but he’s scored a couple of goals and is looking to improve all the time.
“He’s in good form at this moment. We’ll see what happens during the course of the January window, but we’re not actively looking for Jarrod to move on.”
Jackson Irvine has been called up by Australia for the AFC Asian Cup next month, but the midfielder will be able to play at Preston North End on Boxing Day before departing.