Kompany missed the 2-2 draw with Queens Park Rangers and Belgium's qualifier against Wales on the international break.
Pellegrini said that Frank Lampard is also available, but Edin Dzeko, David Silva and Aleksandar Kolorov remain sidelined through injury.
The timing of Kompany's return could be pivotal as City look to hang on to Chelsea's coattails in the title race, and ahead of must-win Champions League tie against Bayern Munich in midweek.
The City boss told reporters: “Vincent Kompany had a small problem but he is available for the game tomorrow. Frank Lampard is also ready to play as well.
"I hope we can return to our normal form now the international break is over.
"Swansea are a very good technical side and we are expecting a difficult afternoon."
It could prove to be a pivotal week in City's season as they try and build up the same kind of momentum that positioned them so well last season to lift their second Premier League crown in three years.
Swansea have made an impressive start to the season themselves and won their last encounter memorably as they came from behind to beat Arsenal at the Liberty Stadium prior to the international break.
Garry Monk's side currently sit in fifth place - three points behind City after an impressive start to the season, and are currently level on points with fourth-place West Ham United.