A host of Premier League clubs – including the likes of West Ham United, Newcastle and Derby County – are said to be keen on signing McCormack ahead of the new season.
The Scotland international was the Championship's top scorer last term, netting 28 times in 46 appearances as he helped Leeds stave off the threat of relegation after a disastrous run of form in early 2014.
Recently-relegated Fulham are thought to have had a £5million bid rejected for the forward, while recent reports have linked Cardiff with a £9million move for a player they sold to Leeds in 2010.
And while Cellino said he may give McCormack the chance to talk to a top tier club if they meet United's valuation, he said he was determined to keep the striker.
"Why should we sell McCormack? He loves it here," Cellino told reporters at the unveiling of Leeds' new head coach, Dave Hockaday, on Thursday.
"If a Premier League team comes we have to give him the chance but I pledge to keep him here.
"He's a beautiful player. Me and McCormack [will] keep our promise to the fans.
"When I make a promise I keep it. Why should I sell him?
"Why should we sell our best players? We have to help Leeds get into the Premier League, so we don't waste our good players.
"[Keeping] McCormack is a matter of principle, not money."
Hockaday – Brian McDermott's successor – has signed a two-year contract at Leeds, despite widespread disapproval amongst fans.