The striker was a huge success at the Stadio Sant'Elia before he left to join Inter in an injury-ravaged spell.
He had announced his return to Sardinia, but something changed for the 31-year-old Honduran.
"Suazo hasn't signed the contract we proposed," President Cellino told Unione Sarda newspaper.
"I don't think it was just his decision, as evidently he was given bad advice. So, if David has any recriminations, he can talk to other people, but not to me.
"Let's be clear, if Suazo had been a player in perfect health, I never would've brought him back, because I tend not to try again with those who have left Cagliari.
"Seeing as he was coming off a difficult year affected by a serious injury, in recognition of all he had done for us in the past, I thought we'd give him a chance to get back to playing football.
"I offered a contract, which in my view was perfectly dignified, and he seemed happy. After a few days, he said he was unsatisfied and would not sign it.
"I can only deduce someone changed his mind. At this point, I am offended and as far as I'm concerned the issue is over."