KANSAS CITY, Mo. (TNS) -- The Royals' next right fielder appears to have arrived.

Alex Rios, a two-time All-Star who spent last season with the Texas Rangers, is close to signing a one-year, $11 million free-agent contract with the Royals, pending a physical, a source close to the negotiations told The Kansas City Star on Monday night.

"They're closing in on the deal," the source said.

The Royals' agreement with Rios was originally reported by CBSSports.com.

Rios, who hit .280 with four home runs and 54 RBIs last season, would answer the team's right-field question. Nori Aoki filled the role last season and hit .285, including a torrid .379 in September, but provided little power.

The Royals sought more pop, and Rios carries a slash line of .278/.323/.439 in 11 major-league seasons.

Rios, who turns 34 in February, spent the first six years of his career with the Toronto Blue Jays, then played four-plus seasons with the Chicago White Sox.

His best years came with the Blue Jays in 2006 and 2007.

In 2006, Rios hit .302, and a year later he produced some of the best power numbers of his career with 24 home runs.

He hit 18 home runs and stole 42 bases for the White Sox and Rangers in 2013.

Rios will join Kendrys Morales, who agreed to a two-year, $17 million deal last week to serve as the Royals' primary designated hitter, and the lineup appears to be set.

The American League champion Royals look for bounce-back seasons from both players. Morales peaked in 2009 with 34 home runs, 108 RBIs and a .306 average, all career bests.