The City captain has struggled with persistent calf problems this season and is expected to be out until at least the end of February.
Kompany returned to action as a substitute against Sunderland on St Stephen’s Day only to have to leave the pitch nine minutes later.
The defender has started just eight Premier League games this season, and the fact City have conceded just once in those matches indicates his value to the team.
The cause of Kompany’s breakdowns is as yet a mystery, with the 29-year-old consulting different specialists in an effort to find an answer.
Pellegrini said: “He is very concerned, which is why he’s trying to recover as soon as he can.
“He’s doing all different examinations to try and understand the reasons why he is having so many injuries.
“Of course he wants to play. He is a very professional player.
“He is the first one who is very worried about his situation, which is why he is going everywhere to ask different specialists what is the reason.
“I think that is the professional way to work when you have problems that don’t allow you to play in your normal way.
“I think you must find every way to see if you can find a solution.
“Maybe there’s not a solution or maybe this can be his last injury but I think he has a very good attitude and he is doing everything he can to return as soon as he can.”
Pellegrini accepts it is not ideal to have a captain that is unable to influence matches but he is not thinking of replacing Kompany.
The City boss said: “I think if he is the captain it is because he deserves to be the captain. Of course, it’s better to have a captain that is always (playing).
“But I think he deserves to have a lot of support at this time and not try to criticise by taking the captaincy away.
“I think that as a captain it’s better to be in front of your team every game but you can also work a lot during the week as a captain when you are injured.”
Pellegrini, meanwhile, has denied Premier League rivals have worked his team out.
City were held to a goalless draw by Everton on Wednesday despite dominating and remain three points behind league leaders Arsenal.
But Pellegrini is confident that was an aberration, saying: “One of the things this team is not is predictable. We have so many different ways to play — with two strikers, with one striker, without strikers.
“We’ve changed the tactical system a lot of times so I think we continue being, after three seasons when I’m in charge, the top scoring team of the Premier League.
“Not only at home but away also, we always try to be an offensive team.
“If we don’t score once, having 17 shots at goal, it’s just an accident, but I don’t think it’s because our rivals know the way they must play.
“Not one team in the Premier League has played against our team hand to hand, they are always waiting for us, with eight or nine players behind the ball near their box.
“We try to make the movement to create space.”
City face Crystal Palace today for the third time this season.
They secured a late win in the league at Selhurst Park in September before a 5-1 victory in the Capital One Cup.
Nigerian striker Kelechi Iheanacho has scored in both games, and Pellegrini could be tempted to give him more game time this weekend.
The City boss said: “I always say with young players, if they are working every day with the team and they play some games, they must take their chance, and I think every time Kelechi has played, he has done very well.”
Palace boss Alan Pardew remains without the injured Bolasie for today’s game but could again have Dwight Gayle available after the forward’s return to training.
He is a reported target for Norwich but the manager said: “He’s been linked many, many times — but we haven’t had an official bid for Dwight.”