The Tigers had been hoping to offload some players as well as reducing their wage bill in the January window, but consider summer signing Hunt too important to their hopes to sell to a rival.
Hunt scored against Wolves in the teams' 2-2 draw at the weekend and Horton now hopes he can continue his good form as they look to move out of the bottom three.
'The club have received a verbal offer of £5million for Stephen Hunt.This has been completely rejected and we're not expecting any furtherbids,' he said.
Keeping in the Hunt: Irish midfielder is happy to let his football do the talking
'That's the end of it I suppose, unless they come in with something very quickly. That's how it stands.
'Unless it's an offer you feel is one you completely have to take, no manager wants to sell his best players so that is the end of the story with Stephen Hunt.
'You heard the press he got from one of his former team-mates, the goalkeeper (Marcus) Hahnemann at the weekend about what a good player he was and if they got him they would stay up and if we kept him we would stay up. Let's hope that's the case.'
Hunt, meanwhile, who has now been the subject of four offers from Wolves, has refused to consider any transfer talk.
'I gather the clubs have been talking a bit but for what I know, I'm staying,' said the Republic of Ireland international. 'In the past I've got involved in transfers and mucked my head up but I've pretty much said nothing this time, got my head down and let my football do the talking.'
Horton also confirmed that midfielder Peter Halmosi has returned to former club Szombathelyi Halafas on loan until the end of the season and that striker Daniel Cousin was in talks with an unnamed club.
City later confirmed Cousin had joined Greek side Larissa on loan until the end of the season with a view to a permanent move.
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