The Hoops are in the market for a new goalkeeper after seeing highly-rated Pole Artur Boruc leave the club this summer.
It had been suggested that Magpies shot-stopper Harper was a potential target for Neil Lennon, having proved to be a reliable and consistent last line of defence down the years.
However, after 17 years of loyal service at St James' Park, Hughton is confident the 33-year-old will remain in the North East.
He told Sky Sports News: "Steve Harper has been a wonderful servant for this football club. He, I think, more than anybody is delighted to see the club back in the Premiership and it's a wonderful opportunity for him.
"He was in very good form last season, he was one of our big players, and we look forward to him having a good Premiership season."
Pressed on whether Celtic had made any contact regarding Harper, Hughton added: "No we haven't had any. As normal there is a lot of speculation but it's something that you expect at this stage of the season. He is very much our goalkeeper and he is looking forward to having a good Premiership season."
Hughton is more concerned with getting players in than letting them go, with Newcastle looking to build a squad capable of holding their own back in the top flight.
"We know it's a difficult time at the moment, everybody is assessing what they have got and what they can move on and what they need to bring in," said the Magpies boss.
"My responsibility here at this club is to bring in what we need to supplement what we already have. We were delighted with the squad we had last season and it's about making additions to that, as opposed to some leaving."
Among those mentioned as possible new recruits is Sol Campbell, who Hughton worked with during their time together at Tottenham Hotspur, and the Newcastle boss admits the veteran centre-half could be an option.
He said: "You never know. We are at that time when we have to make sure we have got a squad that is strong enough. That is all part of the rumour mill, but I'm sure wherever Sol goes he will be a worthy servant."