Nasri will sign a short-term deal worth around £80,000-a-week and his move to the London Stadium will mean a reunion with former teammate Pablo Zabaleta and former manager Manuel Pellegrini, who he played some of his best football under.
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. The former France global received the treatment in December 2016 while on holiday. Then, in August, his ban was extended by a further 12 months.
Meanwhile, West Ham have reinstated their academy coach Mark Phillips after investigating his involvement in a march organised by the Democratic Football Lads Alliance (DFLA).More news: Style nationalism comes under fire at WWI commemorations in Paris
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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.
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.
The club suspended Phillips last month after he attended a DFLA march through central London and later defended the group - which has been accused of Islamophobia and racism - in a series of posts on Twitter.