Nasri will sign a six-month deal until the end of the season with the east London club, which is to contain the option of an additional year thereafter.
But the former France global has encountered a troubled career since, having been banned for 18 months by UEFA for doping.
A month later he was banned, initially for six months, for using an intravenous drip treatment that contravened World Anti-Doping Agency (Wada) rules, leading to a Spanish Anti-Doping investigation. The former France worldwide received the treatment in December 2016 while on holiday.
It is understood that West Ham will bow to wage demands of £80,000 a week, or £5m a year, by Nasri.
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After the global break, West Ham entertain Nasri's former club and current league leaders Manchester City at the London Stadium.
West Ham boss Manuel Pellegrini wants extra fire power up front and worked with the player before at City.
However, according to The Mirror, West Ham have not been left encouraged by the playmaker's current fitness levels and there are doubts over whether Nasri will be available to play in January.
Nasri is a free agent after having his contract with Turkish club Antalyaspor terminated in January after he was handed an 18-month ban for a doping violation.