If the 21-year-old Anglo-Australian, named in a 12-strong squad, accepts the offer, it would effectively end his career at the county and would also make him ineligible to play for England.
The Gloucestershire chief executive Philip August explained: "As I see it, and as the Test and County Cricket Board sees it, it will break his qualification to play for us as an English-based player.
"This means he won't be able to play for us next season because our one overseas player that we are allowed is Courtney Walsh, who happens to be the club's captain, so we couldn't really dump him."
Symonds, born in Birmingham but raised in Australia, where he was a member of the Australian Cricket Academy, will come under pressure to reject the overtures of the country to which he emigrated when just 18 months old. August, speaking on BBC Radio 5 Live, said: "We are, in a decent sort of way, trying to persuade him not to play for Australia A.
"Courtney Walsh will be playing tomorrow for the West Indies against the Australian Prime Minister's XI in Canberra and will be talking to Andrew on our behalf and explaining the benefits of staying within the English county system and playing for Gloucestershire.
"The ball is firmly in Andrew's court. If he accepts the invitation to play for Australia A, the interpretation is that it breaks his qualification and therefore we would not be able to play him next year."Reuse content