But Mike Zimmer says he isn't quite ready to do that.
The Vikings coach addressed the situation Friday in a press conference during rookie minicamp.
"Well, yeah," Zimmer said. "It'll always be an open competition, but with the veteran guys we have, we've been doing Phase II. And he hasn't been working yet, Latavius hasn't. So, we've got a long, long way to go before we make any determinations on any of that."
Minnesota picked up Murray in March during free agency. He signed a three-year, $15 contract with the franchise. Third-year runner Jerick McKinnon is still on the roster and has the most experience in the Vikings' system, but is likely the odd man out when it comes to the starting gig.
Murray likely felt pretty comfortable with his chances before the second round of the 2017 NFL Draft last weekend, when the Vikings chose to trade up in the round to snag Florida State star Dalvin Cook. The Seminoles' all-time leading rusher was widely considered one of the top prospects available at the position, but slid down on draft boards due to off-field and injury concerns.
Zimmer said Cook showed "acceleration, good feet and good vision." The Vikings hired new running backs coach Kennedy Polamalu in January to replace Kevin Stefanski, who moved to quarterbacks coach. Kennedy is Troy Polamalu's uncle.
But Cook told reporters that starting isn't his "ultimate goal."
"My ultimate goal is to find my role, just come in and contribute to the team anywhere possible and help the team win," Cook said. "That's my ultimate goal."
Peterson had at least 200 carries for the Vikings in eight of the last 10 seasons. He had at least 230 carries seven times and eclipsed 300 carries four times, since 2007. In 2015, Peterson led the NFL with 327 carries. Last season, McKinnon led the offense with 159 carries, while Matt Asiata chipped in 121 carries.