The likes of Fulham, West Ham United, Cardiff City and Newcastle United have all been linked with moves for the Leeds captain, who was the Championship's top scorer with 28 in 46 appearances last term.
Fulham are said to have made a £10 million offer for the Scotland international and reports emanating on Wednesday suggested McCormack had lodged a transfer request.
But Cellino maintained his stance on the in-demand forward on Thursday, stating that the club were keen on keeping him at Elland Road.
A club statement read: "Leeds United owner Massimo Cellino and the club would like to respond to recent media speculation regarding Ross McCormack.
"We would like to reiterate our desire to keep Ross McCormack at Leeds United.
"This desire includes keeping all of our best players as we look to build a stronger and successful squad for the 2014/15 Championship season.
"Leeds United may not be the richest club in the Championship, but we do not need to sell our best players in order to run the club successfully."
Cellino bought Leeds in February but was initially rejected by the Football League after failing an "owners and directors test".
The Italian - who formerly owned Cagliari - successfully appealed the decision in April, before parting company with manager Brian McDermott and appointing Dave Hockaday as the club's new head coach last month.
