The Barcelona star is set to return to the Upton Park club, but only if he passes a medical.
The 27-year-old spent last season on loan with the London side and has been linked with Everton.
Song, who played for Arsenal between 2005 and 2012, will sign a three-year contract if he can prove his fitness.
“We just hope the medical shows he’s in a sufficient state for us to gamble,” West Ham co-owner David Sullivan told the Knees Up Mother Brown Podcast.
“He couldn’t physically pass a medical tomorrow, but if the medics say it’s just a technical thing and he’s only a couple of weeks away you’d take that gamble and hope they’re right.”
Sullivan said signing Song on a three-year deal would be a “huge commitment”, adding: “He’s a big earner.”