Former West Ham striker Carlton Cole says Samir Nasri is a "classy player" who would "bring something different" to the club.
Sky sources understand ex-Manchester City and Arsenal midfielder Nasri is currently training with the Hammers as he attempts to win a six-month, £80,000-per-week contract after 18 months out of the game.
The 31-year-old former France international was banned from football for breaching World Anti-Doping Agency (WADA) rules in 2016 but is free play again from January 1 and underwent a medical in London last week.
Nasri played under current West Ham boss Manuel Pellegrini at City, where the pair won the Premier League and Carabao Cup double in the 2013/14 season, and Cole believes the Hammers should give him a chance.
"I think the manager has a good relationship with him," Cole told Sky Sports. "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."
Nasri's potential arrival could coincide with a player leaving in the opposite direction as star forward Marko Arnautovic hinted on Wednesday that he may be ready to quit in order to chase his dream of playing Champions League football.
Former Hammers Jack Collison and Hayden Mullins said on Sunday that the club must do whatever they can to keep Arnautovic and build their team around him, something Cole agreed with.
"Do you know what, he's happy at this club," Cole added. "I don't think he's looking actively to go and leave. He's loved here.
"I don't see any reason why he should be leaving the club. Everyone knows what he's capable of here and I think we'll see him stay.
"If he does go, it will be a great loss to West Ham, but we always find a way to carry on. We always do.
"I don't want him to leave. I don't think the club will let him leave, because he's our main player."
West Ham return to Premier League action after the international break when they host Pep Guardiola's City on Saturday.
The Hammers made a slow start to the season but have steadily improved and now find themselves 13th on 12 points after their opening 12 games and Cole believes Pellegrini has done a "great job" since taking over in the summer.
"You've got to understand, he's come in, he's had a hard job already," Cole said. "We didn't start too well but you've got to put that down to the players gelling.
"We've had a load of new players come in and as we saw with Everton it didn't bode well for them [last season].
"They were struggling when they brought their players in, Sam Allardyce went over to steady the ship, it was a little bit like that.
"When you bring a load of players in, to get them gelling together all of a sudden is a big task. I think the manager has done a great job so far and we are going places."
Cole was speaking at the first ever West Ham United eSports Cup, powered by Basset & Gold final.