McCormack, who topped the Championship's scoring charts last season with 28 goals, has been heavily linked with an exit from Elland Road in recent transfer windows.
Alan Pardew's side were the latest club reported to have shown an interest in the Scotland international, while Leeds rejected bids from Cardiff and West Ham in January.
The striker penned a new three-year contract last summer and has insisted on numerous occasions that he is happy to stay in West Yorkshire, although he does have Premier League ambitions.
Cellino is currently looking to install a new head coach following Brian McDermott's departure, and he recently met with the United squad to discuss plans for the new season amid uncertainty surrounding the club's finances as players were not paid on time for May.
The Italian, who is finalising the sale of Serie A side Cagliari in order to focus on Leeds, sees McCormack as a big part of the club's future and insists that he will be staying put.
"Newcastle made an offer for McCormack and I said no," he said.
"He is happy to stay here and that made me proud."