The 27-year-old England international has been in talks with the Premier League champions over extending his current deal, which runs until the summer of 2016.
Pellegrini said ahead of Saturday's clash with Everton: "I always said it is important for this club to keep Joe with us.
"He is a very good goalkeeper and not only a very good goalkeeper, he is a very important player for the squad also. So — maybe — in the next day you will have good news.
"Joe is having a very good season. The arrival of Willy Caballero was very important for the club, for Joe, for Willy, for everyone — because he is a very good goalkeeper.
"I think the best way for players to have high performance is when they have important competition. I think that was very useful for him and I am very happy about that."
City will be without influential captain Vincent Kompany for the Toffees' visit to Etihad Stadium after the Belgium defender sustained a hamstring injury.
The Chilean added: "Vincent, maybe in the way he plays, is more exposed to having injuries because he plays always with 100 per cent intensity and he works every day in the same way.
"But we hope for the same that happened last season — he will manage those injuries. They are important injuries but not very long injuries."