The ornate twin tower complex has more than 450,000 square feet of space.
The Wrigley Company announced last month that it will move out of its offices at its namesake building and relocate to Goose Island.
Crain's Chicago Business reports that Groupon would occupy part of the building while keeping its office at the former Montgomery Ward Building on Chicago Avenue.
Real estate experts say the Wrigley Building is worth up to $45 million.
