West Ham boss Manuel Pellegrini wants extra fire power up front and worked with the player before at City. It is understood, should he pass the medical, that he will join on a six-month deal with an option to extend his stay.
The Frenchman will soon return from a doping ban, which he picked up for breaching World Anti Doping Agency rules in December 2016 by receiving an intravenous drip of 500 millilitres of water which contained banned nutrients.
While the former France international's ban means he is unable to play until January 1, the terms of Nasri's suspension allow him to train with any club from this month onwards.
It was alleged Nasri received 500 millilitres of hydration in the form of sterile water containing micronutrients while on holiday in the U.S. during a time when he was playing for Sevilla, on load from Manchester City.
Nasri was a regular at Manchester City under the Hammers manager in their title-winning campaign in 2014.
His last competitive appearance came for Antalyaspor on November 26 a year ago.
Nasri, who made his name in England with West Ham's London rivals Arsenal after joining from Marseille, left Turkish side Antalya in January after a disappointing six-month spell following his arrival from City.