Campbell has had a major impact at the KC Stadium after spending much of the season on loan from Manchester United.
He has scored 15 goals for the Tigers and created the winner for Dean Windass in Saturday's play-off final victory over Bristol City at Wembley.
"I'll be doing business with United boss Sir Alex Ferguson," said Brown.
"I don't know if Fraizer will stay, that is for the manager of the European champions to decide.
"It is obvious that he is a talent and we want to keep him and I would have thought that we had the money to buy him now, but that is not my decision.
"He is top of my shopping list and I have promised the players who got us into the Premier League that they will be given their chance.
"We have a good nucleus, but I will add to the squad with players who will improve us on the field and off the field."