West Ham's head of medical and sports science has provided the latest news.
Centre-back Angelo Ogbonna, meanwhile, has entered the final stages of rehabilitation.
The West Ham head of medical and sports science told the official site: "The plan is for Enner to join some parts of team training later in the week and we then hope he will be able to step up his training regime and join in a few full team training sessions next week.
"Injured players also trained in the stadium and we used the stadium stairs to do some good fitness work with Enner and Alex Song.
"Alex is doing fine, working with the ball and is on schedule. Angelo Ogbonna has entered the final stages of rehab and will join full training soon."
It's safe to suggest the latest news won't affect West Ham's first-team selections just yet.
But the update will no doubt come as a boost for the Hammers, who will need as many returning players as they can to help maintain their impressive away form - and help boost their home form.
West Ham's biggest weakness (although it's not much to complain about when you consider they are third in the Premier League) so far this season has been an inability to dictate play and boss games at home.
Enner Valencia will add options when it comes to that kind of scenario, while Alex Song - if he produces his best form - could be crucial as a playmaker.