He travelled to London yesterday accompanied by City medical staff and was assessed by England doctor Ian Beasley and physio Gary Lewin.
It was decided Barry had made sufficient progress to return to the capital at the weekend for further tests.
Barry will not fly to Austria for England's final warm-up game against Japan in Graz on Sunday and has yet to do any running or turning on his right ankle, so it remains uncertain whether he will make South Africa.
Thus far he has been confined to jogging in a swimming pool as he eases his way back towards fitness but has at least discarded the protective boot which was supporting his ankle.
Capello is determined that Barry should be given every chance of making the finals even if he has to miss the opening World Cup clash against the USA in Rustenburg on June 12.
Barry will have a scan on June 1 and Capello has to name his final 23-man squad on the same day.