The Unione Sarda newspaper reported on Saturday that the club and local authorities would work together to make the stadium fit to host Serie A matches by Sept. 21, while they have agreed on a period of 60 days to complete refurbishments.
Final approval will not be issued until the project is endorsed by the Italian National Olympic Committee, which is the country's overall sporting authority.
Once that has been achieved, the city council will approve the plans plus any modifications requested by CONI, before the provincial authorities give the definitive green light.
However, as the Cagliari province has reportedly already given their unofficial go-ahead, the club are effectively waiting for CONI's word before starting work.
The move would end a long-running saga which has seen Cagliari play its "home" matches on the Italian mainland after abandoning the dilapidated Stadio Sant'Elia last year due to disagreements with the local authorities and safety concerns.
Last season, club president Massimo Cellino was arrested and charged with embezzlement and false representation over the rebuilding of the ill-fated Is Arenas stadium, where Cagliari had planned to relocate before the campaign kicked off.
The mayor of Quartu Sant'Elena, where the ground is located, and a councillor were also arrested for their involvement in the case.
In May, Cellino was banned from the sport for four months by the Italian Soccer Federation for allowing the sale of tickets for last September's match with AS Roma that was supposed to be played behind closed doors.
After a series of rows, the club eventually had to temporarily relocate to the Stadio Nereo Rocco in Trieste, which is 1,000 kilometres away from Cagliari and near Italy's border with Slovenia.
Cagliari are due to host Sampdoria in their next home match on September 21.