Wigan reportedly offered in the region of £1million for Brayford, who is out of contract at Pride Park in 12 months' time.
Derby boss Clough does not want to lose the 25-year-old for nothing next summer and has already held initial talks regarding a new deal.
Cardiff City, Stoke City and West Ham United have also been linked with Brayford in the past, but Clough is optimistic that the former Crewe Alexandra defender will stay with the Rams.
"We had an offer that was swiftly rejected," said Clough in the Derby Evening Telegraph. "If an offer came in that did meet our valuation, it would then be up to John.
"What we can't afford to do with players is let them go for nothing in 12 months' time. He's got 12 months to go, he's been brilliant for us and he's entitled to go and have a look around and see what's on offer.
"But we think he will end up staying - we hope he will - and we're not under any pressure to accept a bid.
"There's no indication from the player that he wants to leave - quite the opposite.
"If he doesn't fancy it (a move), we will sit down and talk about a new deal any time he wants. We've had initial talks with him but we said, 'let's just see what happens over the next few weeks'.
"There was previously some interest from the league above as well and, at 25, he's earned the right to see what's out there - but we hope he'll remain with us."