Nasri, 31, is currently training with Manuel Pellegrini's side as he hopes to win a six-month contract with West Ham after 18 months out of the game.
The Frenchman underwent a medical in London last week and will be able to play once again from the start of January. He is still serving a ban from the sport for breaching anti-doping regulation in 2016.
The midfielder played under Pellegrini at Manchester City, winning a league and cup double in 2013/4, something that has prompted Carlton Cole to believe in Nasri.
Speaking to 'Sky Sports', Cole remarked: "I think the manager has a good relationship with him. We know his class, he's a classy player.
"He will bring something different to the squad and he has that experience too.
"It will be a great addition to the squad but it depends what the manager wants and what the owners want."