Cellino said he would leave jail only when he was recognised as being innocent. He was arrested two weeks ago along with Mauro Contini, the mayor of Quartu Sant'Elena, the district where the stadium is located, and councillor Stefano Lilliu.
The trio were jailed after being charged with embezzlement and false representation over the rebuilding of the stadium which became the Sardinian club's home at the start of the season.
"Cellino has decided he wants to leave (prison) only when it is recognised that has nothing to do with the charges because he has not done anything illegal," his lawyer Benedetto Balleri was quoted as telling the ANSA news agency on Friday.
All three were granted release from prison by the Court of Review and placed under house arrest on Friday after being refused bail last week by a judge but Cellino subsequently decided to stay in jail.
The small Is Arenas ground, which hosted third-tier matches in the 1980s, has only one permanent stand.
Three temporary stands were built but Cagliari's first match against Atalanta had to be staged behind closed doors after local authorities ruled the venue was not ready.
The following match against AS Roma was cancelled by the Cagliari city government after the club defied orders to play the fixture without supporters.
Cellino told fans the ground was safe, invited them to turn up for the game and accused the city government of placing bureaucratic obstacles in the club's way.
Roma were awarded a 3-0 win but the club president won a court case last week which could lead to the game having to be played after all.
Cagliari were banned from hosting a game against champions Juventus and had to switch the fixture to Parma.
The match against AC Milan on Feb. 10. was initially due to be moved to Turin amid security worries but eventually went ahead at Is Arenas after a regional tribunal ruled it was safe.
Cagliari played at the Stadio Sant'Elia from 1970 until midway through last season when they left because of disagreements with the local authorities and growing safety worries.
The club hosted the remaining matches last term in Trieste, near the border with Slovenia and nearly 1,000-km away on the Italian mainland.
Last Sunday Cagliari, 13th in the 20-team league, beat Torino 4-3 behind closed doors after the club asked fans to stay away from the stadium.
Cagliari travel to 14th-placed Bologna this Sunday.