The 31-year-old midfielder is a free agent due to his contract with Turkish side Antalyaspor being ripped up after he was slapped with an 18-month ban for breaching WADA doping rules.
Nasri received an intravenous drip in Los Angeles by the Drip Doctors two years ago while on loan at Sevilla from Manchester City.
His ban is due to finish at the end of December and the former French international is desperate for his old City boss Manuel Pellegrini to throw him a lifeline.
However, the Mirror claims the Hammers have concerns over his fitness after rocking up to the London Stadium “overweight”.
Pellegrini is keen to work with Nasri again who has not kicked a ball in anger for two years.
West Ham will give him the chance to earn a lucrative £80,000-a-week six-month deal if he proves his fitness before the January transfer window opens.
A fit Nasri with the quality he brings could be a smart piece of business for the Londoner’s and would save shelling out millions on a transfer fee for a player with a similar profile.
The playmaker is training with the Hammers at their Rush Green base and will be given every chance to impress before the turn of the year.
West Ham boss Pellegrini is keen to bolster his injury-hit squad in the winter market.
Argentine playmaker Manuel Lanzini remains on the recovery trail after getting injured before last summer’s World Cup.
Big summer signing Andriy Yarmolenko faces the rest of the season out, alongside fellow August arrival Carlos Sanchez.
West Ham fans have voiced their frustration on social media about Nasri’s potential arrival in East London.
But the Premier League winner will not get eh chance to pull on the Hammers shirt unless he proves his fitness over the next two months.
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