"He's meant to be really popular with the players and I think Pellegrini has set his heart on signing him.
"I think he will come. He's proven his fitness and he has a desire to come so I think Pellegrini wants to recapture that form he showed for him at Manchester City."
Nasri was allowed to start training again in November after completing an 18-month doping ban.
The 31-year-old former Arsenal midfielder is likely to join the Hammers for an initial six months with the option to extend.
Manuel Pellegrini is keen to reunite with Samir Nasri in January (Image: GETTY)
Samir Nasri only made eight apperances for Antalyaspor (Image: GETTY)
The Frenchman last played for Turkish club Antalyaspor, but his contract was terminated on January 31 this year.
A month later he was banned for for using an intravenous drip treatment that contravened World Anti-Doping Agency rules.
In other Hammers transfer news, Express Sport understand the club have been told they must pay £20million if they want to bring in Nantes striker Emiliano Sala.
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Nantes striker Emiliano Sala is another player West Ham could sign in January (Image: GETTY)
Sala has been in blistering form in Ligue 1 this season with 12 goals from 15 games, making him joint top scorer with Kylian Mbappe.
Hammers boss Pellegrini is without injured striker Marko Arnautovic for a month and wants to add more firepower to his side and Argentina international Sala, 28, is his preferred choice.
Everton, Burnley and Cardiff, who have already made an offer, are also in the hunt but West Ham are at the front of the queue and Sala is said to be keen on a move to the Premier League.