Doubt was cast over the future of the 32-year-old, who recently decided to move his family back to his native Carlisle.
Norwich also forked out £8.5 million in March to sign Dutch international striker Ricky van Wolfswinkel from Sporting Lisbon.
Wolfswinkel arrives at the club on July 1 and, with Hughton having played a lone striker up front for much of the current season, Holt's place could be under threat.
Hughton said: "All I've seen is some press speculation What we have in Grant is someone who has signed a contract in the summer.
"He has two years left of his contract. I think he started more games than he did last season so this is somebody who is right in there playing games.
"Anything that is heard or written about is very much speculation. For me it has not been an issue."
Hughton, whose side clinched Premier League safety at the weekend with a 4-0 win against West Brom, wrap up their season on Sunday with a trip to managerless Manchester City.
The Norwich boss is expecting a tough match despite the departure of former City boss Roberto Mancini following the FA Cup final defeat to Wigan last Saturday.
Hughton said: "I was surprised that Mancini went. There seems to be a fair bit of stability at Manchester City and with the plans that they have for the stadium and the area it seems that they (the owners) are there for the long haul which is a good sign in our game.
"The players are quality players. They are guaranteed second place. It's their last home game of the season and they will certainly want to finish on a high.
"The odds are against us because they don't lose many games at home."
Norwich goalkeeper John Ruddy, who started against West Brom following a long-lay-off with a thigh injury, is expected to start against City.
Ruddy was left out of the England squad for the friendlies against Republic of Ireland and Brazil, but Hughton believes he is still in Roy Hodgson's international plans.
Hughton said: "I'm sure he is still right in there amongst it, but for John it is very much about pre-season, getting back in the team, playing games and I am quite sure he is right there in contention."
Hughton, whose side could finish as high as 12th, is determined to strengthen his squad in the summer.
"I have a responsibility to keep improving," Hughton said. "We'll try to be as busy as we can. How many that sees us bring in we don't know.
"When we look at the season as a whole defensively we held our own. We needed to get the goals that could win us games. That is from the team not just individuals. We must turn some of the draws into wins.
"But everybody over the summer will be trying to strengthen their squad. There will be lots of decisions to make. The nucleus is there, it's just trying to develop."