Stoke City manager Tony Pulis is reportedly keen to bring in Carroll has a replacement for James Beattie.
“I wouldn’t be prepared to sell him,” said Hughton.
“It’s always a worry that other clubs will be interested in your players, but there hasn’t been a bid and we’d certainly be grateful if that’s the same come the end of the window.
“If there is, then it’s testament to what these lads have done so far, but I don’t envisage anyone leaving.”