The NHL is reportedly moving the 2020 NHL Entry Draft up a few days from October 9th-10th, 2020 to October 6th-7th, 2020. This is according to a report from Sportsnet NHL insider Elliotte Friedman.
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No indication why the NHL has made this decision, but I'll presume it's because they feel that the Stanley Cup Final will wrap up earlier than initially anticipated. Rather than have a few days or a week of dead time following the Cup Final and the NHL Entry Draft wouldn't normally be a problem in a normal season, but 2019-20 is anything but a normal season. It's expected that free agency will open the weekend following the Draft, which would be that same October 9th-10th weekend.
No firm dates for the 2020-21 season have been given, but it's expected that training camps will start sometime in mid-November with the season to officially begin on December 1st. Stay tuned.
Tentative dates as of two months ago: