The Australian club are currently working on joining the A-League, but a delay with the paperwork from Football Federation Australia means they cannot enter until the 2018/19 season.
That has put off Drogba, who is currently on the hunt for a new club after leaving MLS side Montreal Impact in November 2016.
The 38-year-old was tempted by the prospect of a move to Australia, but he couldn't face waiting around for South Melbourne to learn their fate.
"We were pretty close," South Melbourne's advisory board chairman Bill Papastergiadis told SBS Australia.
"Terms were agreed, but where we had difficulty was with keeping him interested during the period in which we could not play in the A-League, assuming we are successful in our bid.