The Green Bay Packers are located in the smallest market in all of North America's major professional sports. As such, Lambeau Field and Green Bay as a whole have not been selected to host a Super Bowl, due in large part to a perceived lack of infrastructure.
Up until a few years ago, the thought of hosting an NFL Draft in Green Bay was ludicrous, if only because the league had held that event at Radio City Music Hall for decades. That all changed in 2015, however, when the Draft was moved to Chicago - it has now been held downtown in the Windy City the past two years, but it is apparently going out for bids into the future.
Packers president Mark Murphy has been on the record in the past saying that the team would be interested in hosting the draft in the future and in the past he mentioned the new Titletown District development, which would likely be a big step forward towards events such as that. It now appears that Green Bay is indeed a candidate to host the draft sometime in the next few years - so reports NFL Network's Ian Rapoport, who caught up with Murphy during the NFL's spring owner's meetings:
Talked with #Packers President Mark Murphy about hosting the draft. They're in the mix for '19, after not making final list for '17 or '18— Ian Rapoport (@RapSheet) May 24, 2016
The hallowed halls of Lambeau Field would make for a fascinating venue for the draft, and the event would also likely need to involve the Resch Center across the street. However, it seems likely that the long-term schedule for the Titletown District combined with interest from other cities like Los Angeles and Chicago (again) are primary reasons for Green Bay to be excluded from consideration in the next two years.
As Murphy indicated, though, keep your eyes on 2019, when the developments should be fully wrapped up, better allowing for an influx of NFL fans, players, and media in the spring.