The Belgium international has been ruled out for up to six weeks with a groin injury sustained in their 4-0 thrashing of Newcastle in their opening game of the season.
Kompany himself has stated he is hoping to be back by mid-September but Pellegrini is happy to play a waiting game.
"(There is) nothing new with Vincent," he said. "Doctors said from the beginning it could last for six weeks. We will see next week how he improves but less than one month is impossible."
Pellegrini has received a welcome injury boost, though, with central defender Matija Nastasic able to start against Hull at the Etihad on Saturday after recovering from an ankle problem.
Javi Garcia filled in for him at the heart of the defence but Nastasic, who was an unused substitute for the surprise 3-2 defeat to Cardiff, is expected to return to action.
"Yes, Nastasic is able to play from the beginning," added Pellegrini.
"I think that Javi didn't do badly but he normally plays in midfield. It is Nastasic's position so I think it is better for the team."
Looking ahead to potential deals ahead of Monday's transfer deadline, Pellegrini refused to be drawn on what players, if any, he may be trying to bring to the club.
"There are a lot of names linked with Manchester City. It is not my duty to answer (on) all those names," he said.
"We will see next Monday what will happen. We have some days to bring someone in. We will see what we can do."
As for whether Monday would be a busy day at the club, Pellegrini insisted: "For Manchester City, no. For the rest of the teams, I don't know."