Cook has been linked with Premiership sides Everton and Tottenham.
Paladini said: “We’ve had various offers, but we’ve decided not to sell any of our best players – we want to give John Gregory the best chance of achieving our aims.
“It would have to be a stupid offer for us to sell Lee Cook – he is a major player and look how many of our goals come from his assists.
“If he was playing for a big club, he would be in the national squad – if someone gave me a choice between [Aaron] Lennon, [Shaun] Wright-Phillips or Cook, I’d choose Cook every single time.
“Clubs like Luton and Leeds are selling players and bringing in a few million pounds but, if there’s a shortfall, the board will have to come up with the money.”