Kompany has missed the last five Premier League games for City due to a calf problem, with the side losing three and picking up just two wins, meaning they sit six points behind surprise leaders Leicester City in the table.
City have lost five league games in total this season but have not been beaten when Kompany has taken to the field.
Pellegrini is hopeful the 29-year-old Belgium international will make his return to the City starting XI on Boxing Day.
"Vincent is working the last two days with the squad. I hope that for Saturday he'll be OK," Pellegrini said via the Manchester Evening News.
"With Vincent returning to the team, with David and Sergio playing normally every week I suppose that we are going to continue being an important team for the fight of the title."
After City host Sunderland at the Etihad Stadium, they face four consecutive away games in 12 days, travelling to Leicester and Watford in the league, Everton in the League Cup and then Norwich City in the FA Cup.