The 31-year-old Frenchman has been training with the Hammers for the last few weeks, and Manuel Pellegrini is impressed with how he has reduced his body weight.
The two times Premier League winner is looking to get his career back on track, as he is without a club since being release by Antalyaspor.
With Jack Wilshere all set for another prolonged period on the sidelines with his ankle injury, the Hammers are now ready to offer Nasri a new deal at the London club.
“Samir is working with us very well, he is reducing his weight,” Pellegrini said. “His mentality is to have a spot here in the squad so it is a decision we will make in the next days.”
The former Arsenal man will sign a £60,000 a week deal until the end of the season at West Ham. The club will have an option for another two years, should he impress.
The Sun adds that Nasri could make his West Ham debut in the FA Cup clash against Birmingham City at the London Stadium on January 5.