"Our players have played for two-and-a-half year in the street and for this reason they're all allowed to leave," he told reporters after a 1-1 Serie A draw at home to Napoli.
"Whoever wants to leave I'll give a kiss goodbye, for whoever wants to stay it's their own business.
"I don't care, these players have done too much and for me to keep them here would be an injustice.
"I can't make these players play in a stadium that wouldn't even be fit for a third division team," he added.
"They've had to travel all around Italy for two years because we were not allowed a home stadium. I can't keep anyone in these conditions."
In October Cagliari returned to the Sant'Elia stadium, which had been the club's home since 1970 until a row with the local council saw them kicked out in April last year, after a project to redevelop the ground was approved.
However, much of the stadium is still a building site and the venue is still only fit to host 5,000 fans.
Cellino said one of the club's best players, Belgian midfielder Radja Nainggolan, would be transferred.
"Nainggolan is definitely leaving, there are six or seven teams after him. He'll be gone tomorrow (Sunday), let alone January, and I'll send him away if he doesn't want to leave," he said.
"I don't know where Nainggolan is going and I don't care. He can choose his club, in any case I neither need nor care about money."
The in-form Sardinian side are 11th in the standings after a six-match unbeaten run and Nainggolan has been a target for several clubs, including AS Roma, AC Milan and Fiorentina.
However, the Belgian told Sky Sport Italia on Saturday that he did not want to leave the club.
"You journalists are the ones who should be talk about the transfer market, not me. I haven't received any offers and I am happy to play here at Cagliari," he said.
(Reporting by Terry Daley; Editing by Ken Ferris)
