Ashton Agar and Usman Khawaja are the other two names doing the rounds, as the visitors grapple with injury issues ahead of the third Test here starting Thursday, March 16.
The four-match Border-Gavaskar series is poised at 1-1. While Maxwell has the advantage of being part of the touring squad for the entire trip so far, Stoinis can stake a claim as replacement for Marsh given his all-round skills and strong seam bowling.
Maxwell was not even in the Victorian Shield side at the start of the summer, having been dropped seemingly as a result of his unsuccessful attempt to move north to New South Wales during pre-season.
Stoinis has been the Bushrangers' preferred choice at No. 3 for several seasons and has done so with success - until this season.