Barlow announced the loss of his and wife Dawn's baby Poppy on Monday, before thanking fans for their "overwhelming" support.
Take That remain on the secret bill to play 'Greatest Day' at Sunday's event, according to a source in today's Sun.
"Gary is going through a terrible time. The last week has been awful - as everyone can understand," an insider said.
"The band have been there for him and totally understand if he doesn't do the gig. Take That are on the running order and the organisers are prepared for all eventualities.
"But they all know Gary will be determined to perform."
The 'Back For Good' boyband apparently remain keen to appear, despite having had no time to rehearse following Barlow's tragic news.
"They haven't rehearsed this week for obvious reasons but they are professionals and can turn it on under pressure," the source added.
"It will be a tough call for Gary but everyone will back his decision."
The Spice Girls and George Michael are among the other pop acts expected to play at the event.
Photo gallery - London 2012: