The 70-year-old says that the striker's decision to move abroad quashed any chance of a deal, but admits that he would have tried to sign him had he wanted to stay in England
Drogba completed a transfer to Shanghai Shenhua after securing the Champions League for Chelsea by scoring the winning penalty in a shootout against Bayern Munich in May, and is now set to line up against the Red Devils in a pre-season friendly along with former Chelsea team-mate Nicolas Anelka.
"The decision was his anyway and he said if he was going to leave Chelsea, he wouldn't play for another club in England," Sir Alex told reporters.
"So that answered that question, but I could've been [tempted to move for Drogba]."
United's pre-season tour continues in China after two matches in South Africa, with a 1-0 win over AmaZulu followed by a 1-1 draw with Ajax CT, the latter secured by Bebe's injury-time equaliser.