It had been thought Barry had an appointment with his specialist on Monday to assess his recovery from an ankle ligament injury.
Instead, he will be tested by the England medical staff on Tuesday, with City counterparts also on hand, before a decision is made on whether the 29-year-old has any chance of going to South Africa.
Fabio Capello has already stated that if Barry is likely to be fit for the opening Group C game against the United States in Rustenburg, he will be part of his 23-man Three Lions party that is announced on June 1.
However, if recovery from an innocuous-looking incident during City's home defeat by Tottenham on May 5 is not certain, Capello has a tricky decision to make.
The Italian has previously stated he will not select anyone who would not be capable of facing the United States.
That was before one of the normal members of his starting line-up was struck down.
"Barry is one of the players we want to be fit," said Capello.
"If he is fit, he will come with us. If not, he will stay at home."
The one safety net Capello does have is that FIFA's rules for squad selection allow any player ruled out through injury after the final squads are confirmed to be replaced until 24 hours before the first game.
That individual would not have to come from the 30-man provisional squad that will be on duty for Monday night's friendly against Mexico at Wembley.