While publicly reassuring Bergodi his job was safe until the end of the season, Sebastiani suggested the man who guided the club back into Serie A, Zdenek Zeman, would be an ideal replacement.
Zeman is out of work after leaving Roma, but the Czech tactician is a hero at the Stadio Adriatico after ending the Delfini's 19-year exile from the top flight by winning Serie B with a dynamic side that scored 90 goals in 42 games.
After catching up with Zeman at a golf tournament in Pescara, Sebastiani told La Repubblica: "I have a great relationship with him and we see each other a lot - the meeting wasn't anything to do with his sacking (from Roma).
"The doors are always open to people who have done well for the club and represented us well.
"After he was fired by Roma I found him to be a little bit angry because he believed in the project but couldn't take them forward for whatever reason."
A first win in six could banish the spectre of Zeman for the time being as Bergodi plots to fire Pescara out of the relegation zone with victory over Cagliari on Sunday.
"I told the lads that he would be coach until the end of the season," Sebastiani added.
"Everything depends on what they do on the pitch and they're not missing anything that other teams have. I think we need about 40 points to stay up but a lot of teams could get there."
Bergodi is missing defenders Francesco Modesto and Marco Capuano, midfielder Vladimir Weiss and striker Ferdinando Sforzini through injury for Cagliari's first top-flight visit to the east coast since January 1993.
The Sardinian club threw their full support behind president Massimo Cellino after the Miami-based entrepreneur was arrested as part of an ongoing investigation into the construction of the Stadio Is Arenas.
A club statement read: "All the directors, employees, coaches and players are close to their president Massimo Cellino at this difficult time.
"At the moment we want to say this - come on president, we are with you."
Cagliari are unbeaten in five games but midfielders Daniele Dessena and Daniele Conti, and defender Davide Astori, serve one-match bans on the mainland.