The 33-year-old Murphy became a free agent after finishing the 2018 season with the Cubs, who acquired him in a trade with the Nationals in August.
The Athletic's Ken Rosenthal has reported that Murphy would get a fair amount of playing time at first base for Colorado, which currently has Ian Desmond at the top of its depth chart at that position. DJ LeMahieu, the Rockies' second baseman last season, is also a free agent.
Murphy spent his first seven MLB seasons with the Mets, making the All-Star team in 2014 before exploding at the plate during the team's World Series run the following season. But defensive blunders hindered Murphy's status as a playoff hero, and he ultimately signed a three-year deal with NL East rival Washington before the 2016 season.
The contact hitter had emerged as a possible offseason target for the Yankees, who have an opening in the infield with Didi Gregorius recovering from Tommy John surgery and Manny Machado potentially signing elsewhere.
Murphy enjoyed his best offensive season in his first year with the Nationals, finishing second in NL MVP voting behind Kris Bryant with a .347 batting average, 25 home runs, 104 RBI and an NL-leading .985 OPS.
Murphy missed the first two months of last season after undergoing offseason knee surgery. He was hitting .300 for the Nats when they dealt him to Chicago for minor-league infielder Andruw Monasterio.
In 91 games between the two teams, Murphy tallied 12 homers and 42 RBI with a .299/.336/.454 slash line.