Compton is set to play for Worcestershire against the tourists next week following an agreement between his county Somerset and the Pears.
An England and Wales Cricket Board spokeswoman confirmed the agreement to Press Association, which indicates the 30-year-old remains in the selectors thinking ahead of the first Test on July 10.
Compton's hopes had been hit after he was this week overlooked for England's warm-up game against Essex, which begins on Sunday.
In a press release to announce the team, national selector Geoff Miller indicated that Joe Root was "currently the best opening partner for Alastair Cook".
Compton's response was to hit 81 for Somerset on the opening day of their warm-up game against Australia at Taunton on Wednesday.
Following confirmation he is also set to play for Worcestershire, in a four-day match that begins next Tuesday, Compton could conceivably get three more bats against the Australians to push his Test claims.
Compton made his England debut at the top of the order in India late last year before scoring back-to-back hundreds on the tour of New Zealand.
He struggled in the return two-Test series, however, averaging just 9.75 to create uncertainty over his place in the Ashes.