The Sardinian club's president has told reporters that he will not sell the fan favourites despite significant interest in both players from rival Serie A clubs and England
Astori had been tracked by both former club AC Milan and Premier League outfit Everton following recent further interest from Roma and Napoli.
Nainggolan, meanwhile, has drawn attention from Juventus, Inter and Roma thanks to his stellar performances in Sardinia since arriving from Piacenza in 2010.
However, Cellino has slammed the door shut on any exit talks regarding the two players, telling reporters in Italy: "I don't intend to upset our supporters. Astori and Nainggolan are staying at Cagliari."
The 26-year-old Astori has been at the club for five years after signing from Milan for an eventual fee of €3.5 million (£2.97m) and had been expected to be the subject of a bid of around €15m (£12.7m), while midfielder Nainggolan was being touted as a potential €18m (£15.28m) target for Italian champions Juve.