The Black Cats have had bids of £2.5million and £3million rejected and are understood to have tried again with a £4.5million offer.
But Coppell was adamant the Royals were in a strong enough position to rebuff any attempt to sign the Republic of Ireland international.
Sunderland manager Roy Keane seems determined to recruit the 26-year-old but despite the former Manchester United man's revered status in Ireland Coppell is convinced Hunt would be willing to remain at the Madejski Stadium.
"The reality was that they made a bid but we would like our core players to be happy staying here," he added.
"There are some clubs that, whether we like it or not, when they come calling then it is hard to turn it down, for the club and the player.
"But he has a really strong connection with this club. He was a free transfer from Brentford when we signed him and although there is not a debt by any means he has a good feeling about this place."