Aguero has scored 15 goals in 17 league matches this season, but has not featured since hurting his hamstring against Barcelona in the Champions League last month.
Third-placed City have 67 points, four behind leaders Liverpool and two off second-placed Chelsea with two matches in hand on both.
The return of 25-year-old would give his side a massive boost for the trip to Merseyside, a match that could go a long way to determining who will claim the Premier League title.
“It (Southampton) is too soon for Sergio,” Pellegrini told a news conference on Friday.
“He has trained for only two days and needs more time. Perhaps one week more and he will be perfect for the game against Liverpool.
“We hope he will return and play an important role in our remaining matches but this match has come too soon for him. He needs more work to become 100 percent fit but he will be fine for next weekend.”
Before Liverpool they host eighth-placed Southampton, who are fresh off last week’s 4-0 thrashing of Newcastle.
While the south coast club are unlikely to qualify for Europe and are in no relegation danger, the Chilean is wary of the threat they pose.
“Southampton are a very good team who are playing without pressure who are very comfortable in the table,” he said.
“They cannot be relegated and they can’t qualify for Europe so they are playing with freedom and we are absolutely sure we will have a hard game on Saturday.”
Defender Micah Richards is available for selection, having struggled with a knee injury.
He has not played since the FA Cup defeat by Wigan Athletic in early March.
(Reporting by Josh Reich; editing by Toby Davis)