New Blues boss Jose Mourinho has been linked with the 26-year-old, as he looks to provide cover for veteran Petr Cech, with suggestions a £5million bid had already been lodged
But Hughton maintains he has no intention of selling Norwich's No.1, who missed a large spell of the end of last season with a thigh injury.
"We see very much John's future here and we look forward to him being here," said Hughton, whose squad are set to report back for pre-season this week ahead of a tour to the United States.
"John would be no different to any player we have here. Any interest in any of our players is just a mark and a testament to how well those individuals have done.
"We start back training on Thursday. John is very much part of our plans and will be here. Then we go away to Austria next week and of course John is very much part of that.
"Any interest shown in any of our players is just a mark of how well they have done."
Norwich officially unveiled club recording signing Ricky van Wolfswinkel, captured for £8.5million from Sporting Lisbon, and are also interested in bringing in England U21 winger Nathan Redmond from Birmingham, Hughton's former club.
Club captain Grant Holt has been linked with a move to Premier League newcomers Crystal Palace, while the Canaries are also said to be tracking Sweden international Ola Toivonen at PSV Eindhoven.
Hughton, however, refused to be drawn on any transfer specifics, saying: "We are working very hard behind the scenes.
"We are a club which wants to make progress, that means any areas of the squad we can improve, we will do."