The 23-year-old has impressed for Cagliari since joining the club from Atletico Nacional in 2011.
“Inter are interested in Ibarbo,” Cellino told Tuttosport.
“But the Nerazzurri decided not to invest in new players during the summer.”
He added: “We want to keep our best players at Cagliari rather than sell them.”
Ibarbo’s current contract with Cagliari is set to expire in June 2015.