The Ivory Coast international was linked with a move to the Championship side, but he was caught by surprise and denied being in negotiations
Social media went into overdrive when Villa owner Tony Xia claimed the Championship club were closing in on a "world class" striker.
Chelsea great Drogba emerged as a possible arrival, given he worked under Villa boss Roberto Di Matteo at Stamford Bridge, with the pair winning the 2012 Champions League.
But the 38-year-old Montreal Impact striker dismissed the speculation, using Twitter to apparently distance himself from any possible move.
"Just come out of training at @impactmontreal & a million messages & trending on Twitter saying I was in Birmingham today," Drogba wrote.
Drogba has scored eight goals in 15 MLS games for the Impact this season.
Villa, meanwhile, have started life in England's second tier with one win, two draws and a defeat.