The Arizona Cardinals released Hopkins on May 30.
"If we end up on the same roster, that would be something epic for the NFL," Cook said of a potential union with the five-time Pro Bowl selection and three-time All-Pro.
Cook, 27, joined the Vikings in the second round of the 2017 NFL Draft. The four-time Pro Bowl selection totaled 1,468 yards from scrimmage and 10 scores in 17 starts last season.
He totaled 5,993 rushing yards, 1,794 receiving yards and 52 touchdowns in 73 appearances for the Vikings. He signed a 5-year, $63 million contract extension with the Vikings in 2020.
The star running back said he shares a similar mindset to Hopkins in that they both "want to win."
"The money is going to come and that's going to happen," Cook said. "But like as far as going to lift that [Super Bowl] trophy up, he has the same mindset as me."
Cook said he planned to "reach out to" Hopkins to talk about free agency. He said it would be a "beauty of a situation" to end up on the same roster as the veteran pass-catcher.
"We're trying to go on the roster and trying to go contend," Cook said.
Cook is expected to see interest from several teams this off-season. The Miami Dolphins, New York Jets, Denver Broncos and Dallas Cowboys are among those who have been linked to the running back.
Cook said he was hearing from many other players around the league about joining forces. He also told The Rich Eisen Show that he wants a team that values him, wants to give him the ball and wants to win.
"It's a waiting game at this point," Cook said. "I'm just trying to find the right situation. I don't think there is a rush for anything."
Hopkins, who totaled 717 receiving yards and three touchdowns in nine games last season, previously mentioned interest in the Buffalo Bills, Philadelphia Eagles, Kansas City Chiefs, Baltimore Ravens and Los Angeles Chargers as potential suitors.
He also has been linked to the New England Patriots and Houston Texans.
The Chicago Bears have more than $32 million in cap space, the most in the NFL, according to OverTheCap.com. The Cardinals, Carolina Panthers, Indianapolis Colts and New York Jets are among the others with the most cap space.
NFL teams have until July 17 to sign franchise-tagged players to multi-year contract extensions.
Ezekiel Elliott, Leonard Fournette and Kareem Hunt are among the other free agent running backs available. Kenny Golladay, Julio Jones, Jarvis Landry and Sammy Watkins are among the other wide receivers on the market.
NFL training camps start in late July.