The 34-year-old Zobrist, who was acquired from Oakland before the non-waiver Trade Deadline last month, will become a free agent after the season.
General manager Dayton Moore says for now he will only discuss the topic at the appropriate time, but if the Royals are interested in signing him, they have a few factors in their favor.
One factor is location: Zobrist is a Midwesterner at heart, having grown up in Illinois. And Zobrist actually spent three years of his early life -- ages three through five -- growing up in Belton, Mo., a suburb of Kansas City.
"And I live in the offseason in Nashville, so it's not far," Zobrist said. "I've been back to the Kansas City area a lot in the past. My sisters went to college in the area. My brother went to college in the area. I've got friends there, so there's some ties to the area."
And the more Zobrist hangs around the team and the organization, the more fond he grows of both.
"They have a lot of guys who are young who've come together in the last few years," Zobrist said. "They've got a bullpen -- playing against them I thought was the toughest bullpen in the league.
"The way the front office runs things and the way the coaching staff runs things, it's loose and fun but also structured. It's very professional. The way they go about everything is really good.
"It's fun to be assimilated into a culture like that, because they're already good. I don't need to change anything. They're already headed in the right direction. I just have to be a part of it."
Next year, the Royals could have an opening in right field. Alex Rios and the club have a mutual option for 2016, but the buyout is a relatively cheap $1.5 million. Zobrist said he won't base his decision on a position opening.
"I played a lot of right field with Tampa [Bay]," Zobrist said, "but I feel like my value is that I can do a lot of different things. For me, it's not so much about picking the right position, it's about the team.
"But first, I want to win a World Series here. Then I can think more about the offseason decision."