The Republic of Ireland international has been linked with West Ham and Portsmouth this week, while the return to fitness of Bobby Convey will put pressure on his place in the Reading side.
However, Coppell insists he is not ready to part with Hunt and still views the midfielder as an essential part of his plans.
"Hunty's strength of mentality and his physical fitness have got him through," Coppell told the Reading Chronicle.
"He never stops working hard on his skills. Sometimes people go as far as they can then settle for that, but he proves that's not always the case.
"He shows that with hard work and dedication you can keep improving and he's a key member of the team."
Pompey boss Harry Redknapp has also played down speculation that he was interested in Hunt.
Redknapp said: "I was impressed with him last season but I haven't even thought about him. I don't see why he would be leaving Reading."
Meanwhile, Reading director of football Nicky Hammond fears it may be difficult to bring in players in for the right price this summer.
West Ham's Hayden Mullins is reportedly a £1.5million target, while Thomas Gravesen of Celtic and Watford's Danny Shittu have also been linked.
But Hammond believes Reading could be victims of their own success in the transfer window.
"Players will become more expensive to us because we finished as high as eighth in the Premiership," he told the Evening Post.
"There aren't cheap deals to be done in the Premiership these days."
Sky Sports