The team avoided such a step with three other players earlier in the day by reaching agreements on one-year deals with starter Jeremy Bonderman, first baseman Carlos Pena and reliever Chris Spurling. That leaves Monroe as the only remaining player eligible for arbitration.
Monroe submitted a request for a $3.05 million salary, while the Tigers submitted their offer at $2.45 million.
Tigers vice president and legal counsel John Westhoff said he's had continued talks with Monroe's agent, Adam Katz, and hoped to have a deal.
"I just view this as the next step in the process," Westhoff said.
The two sides still have time to reach an agreement. Hearings don't begin until Feb. 1, and the two sides have until a ruling is issued to work out a deal.
Monroe hit .277 with 20 home runs, 30 doubles and a team-leading 89 RBIs in his first full year as an everyday outfielder. He also led the Majors with 12 sacrifice flies.
Monroe's future in Detroit was relatively secure once the Tigers showed no interest in bringing back free agent left fielder Rondell White, who signed with Minnesota. Monroe is expected to be the everyday left fielder, though Dmitri Young and Curtis Granderson could also see time there.
Jason Beck is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.