The Colombia international has caught the attention of the Nerazzurri with his fine performances in Serie A
The 23-year-old has developed into a key figure at Cagliari since joining the club from Atletico Nacional in 2011 and his good performances have seemingly not gone unnoticed at San Siro, even though they opted against making a move for Ibarbo last summer.
"Inter are interested in Ibarbo," Cellino was quoted as saying by Tuttosport.
"But the Nerazzurri decided not to invest in new players during the summer."
The Cagliari president then hinted that Ibarbo will not be available on the cheap if Inter or any other team make a move for the attacker in the January transfer window.
"We want to keep our best players at Cagliari rather than sell them."
Ibarbo has a contract with Cagliari until June 2015.