If Hughes thought he might be able to bully his former club with a lucrative offer, however, he has been told to think again by Allardyce, who appears determined to hold on to arguably his most prized asset.
Allardyce has held talks with Santa Cruz to clear the air following comments made by the player suggesting he wanted to leave Ewood Park.
Allardyce said: "Roque did an interview that he shouldn't have done and I've told him that. I thought it was really, really poor timing. We've had a chat and I've told him I don't want him to leave. The first thing we need to do is stop the speculation because all we have heard is that Roque Santa Cruz is leaving.
"I would be very reluctant, even if a big money bid came in, to sell him. My gut feeling is that no one will offer enough for us to have to sell him. No amount of money is any good to me because there is no one I can spend it on in that department that will make us better."
Allardyce, meanwhile, has allowed veteran forward Robbie Fowler to leave after telling him he will not be offered a new contract and has also told defensive coach Nigel Winterburn he is also surplus to requirements at Ewood Park.
Allardyce said: "Robbie had not played that many games and his contract was expiring. It was only a short-term thing and I didn't feel it necessary to extend it. I wish Robbie all the best and wherever he goes then hopefully he will score some more goals."
Meanwhile, Lassana Diarra has told Mark Hughes that Manchester City's financial muscle is no match for the glamour of Real Madrid.
Portsmouth midfielder Diarra, 23, will seal a £20m switch to Real in January after agreeing to move to the Spanish giants.
City boss Mark Hughes had been desperate to lure the French star to Eastlands as part of his rebuilding work in the transfer window.
And Diarra admits that City were ready to blow Real out of the water in a bid to tempt him to Manchester.
But the former Chelsea and Arsenal man insists that City were never in the running once Real had made their move to take him to Spain.
Diarra said: "Were Manchester City keen to sign me?
"Yes, indeed and, on a financial level, I would have earned a lot more.
"But Real are very attractive and I believe I have earned respect.
"I was in England for five years and learnt a lot of things there and I became very attached to the Premier League.
"You can't leave it that easily, but Real came, and I was their priority. That makes you think. It is an honour."