Team president Mark Murphy said that the club has applied to host the event in 2019, 2020 or 2021, per ESPN.
"We think it'd be great for the league to have the draft here and celebrate the smallest market in the NFL," said Murphy, who was in attendance for a meeting with Packers shareholders on Thursday.
The draft was held in Chicago for the second consecutive year in April. The NFL has yet to announce any sites for future drafts.
Other cities that have expressed interest in hosting the draft include Atlanta, Chicago, Canton, Dallas, Denver, Jacksonville, Los Angeles, Philadelphia and Pittsburgh.
NFL Commissioner Roger Goodell said in April that the draft likely will leave Chicago in 2017. The event had been held in New York City for 50 consecutive years (1965-2014) before it moved to Chicago in 2015.