"If we do pick first, we're leaning more toward one of those three forwards," Avalanche Executive VP of Hockey Operations Joe Sakic told the newspaper.
"We feel those three forwards are just too good to pass up."
Jones, 18, is the top-ranked North American prospect heading into the June 30 draft. Many believed there was a good chance the team would select him first.
The Post noted the Avalanche's need to bolster its defense and its surplus at the center, and Drouin is the only winger of the three forwards.
The Avalanche has roughly $13 million in available salary cap space and go look to upgrade their blueline via the free agent market or go the trade route this off-season.