New York Yankees 2B Robinson Cano is a career .309 hitter in his nine seasons. (Al Messerschmidt/Getty Images)
The qualifying offer is worth $14.1 million, but Cano has reportedly been seeking a 10-year contract worth over $300 million.
Cano, 31, hit .314 with 27 home runs and 107 RBI last season for Yankees, who did not make the playoffs.
Kuroda went 11-15 with a 3.31 ERA and 150 strikeouts.
The team would receive a compensatory first-round draft choice if the players decline the qualifying offer and sign with another team.
According to the report, the team is not sure about extending an offer to outfielder Curtis Granderson. He only played in 60 games in an injury-filled 2013, finishing with a .229 batting average, seven home runs and 15 RBI.