Currently on a rookie scale deal, Drummond needed to agree an extension before the deadline to avoid becoming a restricted free agent next summer, but he made the decision to give the Pistons more flexibility in the market.
Delaying the extension will allow the Pistons to sign other players and then use their Bird rights to sign Drummond, whose salary would have been included in the books heading into the summer.
"Andre wants to be here long-term," Pistons coach and team president Stan Van Gundy told reporters. "He wants us to have the flexibility to continue to add people to this team.
"Every player says I'm all about winning. This guy is proving it."
Drummond averaged 13.8 points and 13.5 rebounds last season.