The 31-year-old has been training with the Hammers for free to try and rejuvenate his career after he was handed an 18 month doping ban in February.
The pair worked together from 2013-2016 while at Man City and formed a good relationship – with Nasri helping to deliver the Chilean coach a Premier League title in his first season.
And Pellegrini is now hoping he can unearth the 31-year-old's talent to rediscover that form ahead of a potential debut at the turn of the year.
Speaking to the Times, the 65-year-old said: "Samir Nasri is a very technical player who always made a difference.
“He was an important player not only for me and City but also for Arsenal.
"What we need is to recover the real Samir Nasri. If he has no injuries until January 1, when he can play, he can be fit.”
West Ham have been a hit with a series of injuries in recent weeks – and the latest blow came on Monday as Ryan Fredericks was ruled out until the New Year.
Fredericks, who joined from Fulham in the summer, joins Manuel Lanzini, Andriy Yarmolenko, Winston Reid and Carlos Sanchez on the sidelines.
And Pellegrini is hoping the former Sevilla and Man City man can fill the void left by the injuries to his playmakers.
If Nasri does formally join the Hammers he will reportedly be earning £80k-a-week.
Meanwhile, both Andy Carroll and Jack Wilshere could return to the claret and blue outfit against the Citizens.
Both of them have been out for the majority of this season with ankle injuries but are avaialable for Saturday's clash against the champions.
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