Spain striker Negredo's right arm was in a sling after City's 9-0 aggregate Capital One Cup semi-final win over West Ham in midweek.
And Pellegrini admitted he would not be ready for the club's FA Cup fourth-round visit of Watford to the Etihad Stadium on Saturday afternoon, but revealed he should be back to fitness within a week.
The Chilean said: "Alvaro is not ready for Saturday. We will see in the next days how his shoulder reacts from the work he is doing. Maybe in a week he will be okay.
"David Silva has some problems. He is not 100 per cent fit. It is just a precaution, we will not take any risks because he still has some pain in his hamstring."
Pellegrini has consistently played down suggestions City could make a move in the January transfer window to bolster a squad still chasing silverware on all four fronts.
He added: "If we talk about all the offers this club made we have at least eight goalkeepers, five centre-backs, nine forwards. No news for the moment."
It was a similar answer when asked about Joleon Lescott, the England centre-back who has been linked with a move to West Ham.
"Exactly the same - no news," Pellegrini said.
City are back in action again on Wednesday as they visit Tottenham in the Premier League while they have another big encounter against title rivals Chelsea looming on February 3.
And Pellegrini said: "We will see on Saturday how the 11 changes. We are going to make some changes. We have a lot of games during January. It is a very busy month and we will continue making rotations."
"(Watford) is a team that is not in a very good position in the Championship but all the managers know the cup games are different games.
"There is more motivation for a Championship team to beat a Premier League team so I am absolutely sure we are going to have a very difficult game."