The club's hierarchy decided to put Taylor up for sale on Wednesday due to a breakdown in talks about a new contract. It is thought the 24-year-old is holding out for higher wages than the club are willing to offer.
With the transfer window due to close on Tuesday, the club will have to move fast if they are to sell Taylor, but after a young Newcastle side beat Accrington Stanley 3-2 in the Carling Cup, Hughton said he still hoped the matter could be resolved successfully.
Asked if Taylor would be leaving soon, he told Sky Sports: "We hope not. It's very much between Steven's representatives and the club. It was very much a club decision (to put Taylor on the (transfer list) and there's still time to go and I hope it will be resolved.
"His contract talks have broken down between himself, his representatives and the club but that is something we hope can be resolved. He is a very good player and certainly I hope an agreement can be made.
"He is a player that we would certainly like to keep here at the football club. I think there are always going to be things that test us and there will always be other issues, but the important thing is that Steven is a player we would like to see at this football club."
Hughton did not say whether he would include Taylor as part of his 25-man squad if the defender was sold and was more keen to talk about his side's hard-fought win at the Crown Ground.
"We came here with a young side and there was a risk in that but we felt we would have enough quality to get to the next round," he added.
"We could have made it more comfortable for ourselves, particularly in the second half but it was the cup tie we expected."