Republic of Ireland international Given, 34, has lost his Manchester City place to Joe Hart this season and is desperate for regular football.
However, despite seeing 35-year-old Harper, the man who for so long acted as back-up to the Irishman during his 11-and-a-half-year stay on Tyneside, suffer a nasty shoulder injury at Everton on Saturday, Hughton will not be contacting City counterpart Roberto Mancini.
Asked about the speculation, he said: "I can understand that one and it is a very emotional one as well, but no, I can categorically say that won't be happening."
Newcastle's position on Given is perhaps equally understandable with the keeper having finally lost patience with life at St James' in the wake of a humiliating 5-1 home defeat by Liverpool in December 2008.
He made it clear he wanted to play his football elsewhere and eventually got his wish when City pushed through an £8million swoop for him at the end of the following month.
Having waited so long for his chance, Harper and his team-mates suffered the misery of relegation at the end of that season, but he proved a more than capable replacement as they regained their top-flight status at the first attempt.
However, his luck changed for the worse on Saturday when he landed awkwardly after an untidy challenge by striker Jermaine Beckford and damaged a ligament in his shoulder.
The full extent of the injury is still being assessed, but Hughton admitted Harper could face a lengthy spell on the sidelines.
He said: "The important thing for us is to asses where Steve Harper is at this particular moment.
"What we do know is it is a ligament injury to his shoulder. That will be assessed over the next couple of days.
"It is probably a little bit unfair to state how long he will be out for because at this moment, we don't know. But it will be for a period of time.
"It's a massive disappointment for him. He is a player who I felt was the best goalkeeper in the Championship last season.
"He has worked very, very hard to get to the level he has and has started the season very well for us.
"Any significant injury that is going to keep a player out for a period of time is a big blow, particularly when it is the person who is between the posts."
Dutchman Tim Krul took over from Harper at Goodison Park and is likely to retain his place for Wednesday night's Carling Cup third-round trip to Chelsea.
However, with Fraser Forster currently on a season-long loan deal at Celtic with no prospect of any recall until January at the earliest, 20-year-old Swede Ole Soderberg is next in line.
Hughton said: "Tim Krul has come in before and adapted very, very well. He is a young keeper of high ability and I certainly have no worries about him and him performing.
"But we will have to assess it once we are made aware of the extent of Steve's injury.
"Tim is in the squad for the Chelsea game and I have absolutely no worries in putting him in."