Rantanen is a restricted free agent who plays right wing on the Avalanche's top line with center Nathan MacKinnon and left wing Gabriel Landeskog. The 22-year-old had an NHL career-high 87 points (31 goals, 56 assists) in 74 games and 14 points (six goals, eight assists) in 12 Stanley Cup Playoff games.
Colorado general manager Joe Sakic said he met with Rantanen's agent, Mike Liut, at the 2019 NHL Draft in June.
"We prefer long term," Sakic said. "If it has to be short term, it has to be short term. We want to make sure we have him signed. There's a lot of players (in the NHL) in that same situation, a lot of great hockey players that are coming up. We'll just see how all the players and agents handle that. There are comparable numbers that are starting to come in. We're open to different possibilities."