The former Liverpool and Newcastle forward has yet to feature for the Hammers since becoming the club’s record signing for £15million after making his loan switch from Liverpool permanent.
The England forward was assessed by Professor van Dijk, and has been told to step up his recovery work a week after taking off an air boot.
Carroll is understood to finally be walking pain free after suffering a complicated heel injury.
The 24-year-old has been working closely with Belgian physio Lieven Maesschalck since damaging his foot in pre season.
The striker is now working in the therapy pools and going through weight bearing exercises, and is expected to be assessed by van Dijk in three weeks time.
After that assessment, the Hammers will have a scheduled time for his return to action.
Carroll has been a massive miss for Sam Allardyce this season, with the Hammers finding Premier League goals hard to come by.
They travel to Tottenham at the weekend sitting fourth from bottom, without a goal away from home all season and without a Premier League win since the opening day.
Although the Hammers have been reluctant to put a time frame on Carroll’s return to action, they have been left encouraged by the reports following Tuesday’s report.