And Hughton again insisted goalkeeper John Ruddy was not for sale.
Redmond, 19, on Thursday became the Norfolk club's third signing of the summer when he moved from Birmingham, following the permanent deal for on-loan Lazio defender Javier Garrido and a record £8.5million transfer of Holland forward Ricky van Wolfswinkel.
Norwich are expected to continue to be busy in the market, as a £4.8m bid for Sweden attacking midfielder Ola Toivonen is said to have been lodged with PSV Eindhoven, while Lokomotiv Moscow's £6m-rated Senegal striker Dame N'Doye and Blackburn left-back Martin Olsson are two other reported targets for Hughton.
England goalkeeper Ruddy, meanwhile, is very much on Chelsea's radar as new manager Jose Mourinho seeks cover for Petr Cech. The Blues are understood to be ready to improve on their £5m offer which was rejected. Captain Grant Holt has also been linked with a move away from Carrow Road.
Hughton, however, stressed he was looking to further bolster his squad ahead of their training camp in Austria and a three-match pre-season tour to the United States.
"We have got no particular number on how many more will come in. We are no different to anybody else. We won't bring in unless we feel it benefits us," Hughton told a press conference.
"The target is always to bring in players as soon as possible to integrate them into the squad.
"If you look across the Premier League some have done good business, others have hardly done any. It really is about using the period of time you are allowed in the best way. That means we are allowed until the end of August, but I want to stress again it is about adding to what we have and we are happy with what we have here already. If we can do it earlier, then great."
Hughton, though, went on the defensive when asked if bids had been lodged for any of his key men.
The Norwich boss said: "No, and probably if there was I wouldn't say it.
"The best way is to conduct business behind closed doors.
"You see we have been able to present Ricky and Nathan as done deals this week and that is fact.
"Around those sort of transfers there is only a small fraction of what you hear that is actually fact. By far the vast majority is very much speculation.
"If there has been interest in our players then that is a plus as far as I am concerned because we must be doing something right.
"I think if there is speculation regarding players we want to bring in it indicates we are attempting to do some work - some of those names will come into the public domain, but the majority will not."
Norwich have seen some departures this summer, with several fringe players moving on, such as striker James Vaughan who yesterday signed a permanent deal with Huddersfield following a loan spell at the Championship club.
Hughton, though, was disappointed not to have been able to retain the services of highly rated goalkeeper Jed Steer, who rejected a new deal to move on to Aston Villa where he will play under former Canaries manager Paul Lambert.
Norwich are, however, entitled to compensation for the 20-year-old, who came through the club's academy.
"I was sad to see him go," said Hughton, who will now look to bring in some goalkeeping cover. "We did offer him a contract, but we all know that is the nature of the game.
"You can do your best that you can, but ultimately it is down to the players."