The 59-year-old Chilean signed off from current club Malaga with a 4-1 defeat at Barcelona on the final day of La Liga season.
Pellegrini said after the defeat: "We will see from Monday onwards where my future goes. When an agreement is reached, we will say something definite.
"I'm not confiming anything, because I don't think it's fitting to speak on the basis of speculation. I have an agreement to start talks with Manchester City.
"Other rumours will be true, others not. But I've focused on Malaga until now."
He continued: "It's going to be tough to leave Spain after nine years. It's a country that has treated me marvellously well.
"A very important stage of my career has finished and destiny willl surely take me to another country."
City chairman Khaldoon Al Mubarak yesterday confirmed he expects to announce the club's new manager within 10 days.
He said: "We obviously want sustainable success for this club and (picking the manager) is absolutely the most important decision for a football club.
"The type of person we would like running our football team is someone with great man-management capability and the ability to get the best out of the talent we have, get the best out of the youth we have and establish and continue a systematic approach from the youth team to the elite team and reserves.
"We have a wonderful team running this process internally (to select a new manager) and are putting a very comprehensive process in place.
"They have created a shortlist of managers who fit that criteria and we are pretty much done. We are very close. I expect to make an appointment probably in the next two weeks.''