According to the report, Infante will receive a four-year deal worth $30 million.
Infante hit .318 with 10 home runs and 51 RBIs in 118 games with the Detroit Tigers last season.
The New York Yankees also were reportedly interested in Infante, offering him a three-year, $24 million deal. Infante can play multiple positions in the infield, but has played 60 percent of his time at second baseman.
Infante is an upgrade over anything the Royals put out at second base last season. The team's second basemen hit .243 with only four home runs in 2013.