Barnett has not travelled with the rest of the Canaries squad for their pre-season tour of America.
He still has a year remaining on his Carrow Road contract but, after seeing out the 2012/13 campaign on loan at Cardiff City, he has been informed that he is free to find himself another club during the current transfer window.
Hughton said in the Pink Un: "At the moment he is not in my plans. He has shown a desire to play regular football, and of course I can understand that.
"He went out on loan to Cardiff and what he would like to do is go and play somewhere where he is going to start on a regular basis. That is simply the only reason we have not brought Leon out here to America.
"He is a good trainer, he works hard every day and I have no problems on that score, but certainly at this moment he is not one that would be in my plans for the season."
While Barnett could soon be heading through the exits, Hughton admits he is working hard to bring further fresh faces into his ranks - with forward-thinking talent top of his wish list.
He added: "What I can say is there are no done deals but certainly the reason I came away a little bit later was because I felt I needed to be in the UK as we try to do some business. But certainly at this moment, no done deals."
On reports linking Norwich with Juventus forward Fabio Quagliarella and Catania's Maxi Lopez, Hughton said: "Yes, I have seen the reports that I was in Italy.
"There are players that we would have an interest in bringing to the club, but wanting to bring someone here and actually getting them is two different things.
"The areas that we felt we needed to improve were the offensive areas. We brought Ricky (van Wolfswinkel) in but on the other side of it Simeon (Jackson) and Holty (Grant Holt) have departed so, yes, the forward area is one we are looking to do something."