ESPNdeportes.com reporter Enrique Rojas cited an unnamed source as saying Guillen wanted out pronto, and that he and Hillman were not on speaking terms.
Addressing reporters on Tuesday, Guillen called the report "completely untrue." Hillman said he was "surprised" and it was "news to me."
Guillen, a mercurial figure in his 12-year career, signed a three-year, $36 million contract last winter as the Royals sought to add lineup punch. In his 100 games, Guillen leads the club with 14 home runs and 69 RBIs.
"Trust me, if I want to say I want out of Kansas City, you guys know me already. I can go straight to the GM or the owners and say, 'Get me out,'" Guillen told reporters.
"But it's unfortunate that some unknown source says that I want out of here. Trust me, when that time comes -- and I hope it never comes when I say I don't want be here -- I just go through all you guys and say I don't want to be here."
Guillen said he talks to Hillman almost every day and acknowledged they have had differences.
But he insisted: "I'm happy here. I'm fine. Unfortunately, this type of stuff comes up, and I'm fine, that's all I can say."
Hillman said he met with a "visibly upset" Guillen on Tuesday to discuss the matter.
"Jose Guillen and I have never yelled at one another, we've never had cross words at each other. We've had differences of opinion, but he's expressed his differences very professionally and so have I," Hillman said.
Guillen said that after such discussions he does whatever Hillman asked him to do.
"I just work here," Guillen said.
General manager Dayton Moore was kept apprised of the story in Kansas City, where he was sorting through Trade Deadline possibilities.
"What I'd say is simply this," Moore said by phone. "We're glad that Jose is on our baseball team, and I look forward to him continuing to produce."
Guillen this season has blasted teammates as "babies" in a profanity-laced rant, said he could "care less" about fans that booed him and then apologized to them, admitted to reporting to Spring Training overweight, and generally has kept the pot stirring. All that after sweating out a suspension for violating baseball's drug policies and being pardoned.
This week he created a stir by saying he preferred playing on the road rather than at Kauffman Stadium.
"Sometimes I just feel more comfortable playing away than home. I just like to play away more than home. That's just me," he said when asked about that on Tuesday. "I have my kids and my family there in Kansas City, but, to me, it's not been too much fun playing at home."
Not only has he sometimes been booed at Kauffman, he's not hit as well there (five homers, 25 RBIs, .254) as on the road (nine homers, 44 RBIs, .266).
And now this.
"I never asked for trade. You can trust me on this. If that time comes that I feel I cannot be here, I'm not afraid to speak my mind. I'm not afraid to speak the truth," Guillen said.
"Just to make it clear. I know Trey and myself have our differences, and we're not on the same page and sometimes I have to live with that because he's my boss, he's manager and I have to do whatever he asks me to do."
Guillen said he had tried several times, unsuccessfully, to contact the reporter Rojas to question him about the story.
Footnote: Hillman listed Guillen as the left fielder for Tuesday night's game against the Oakland A's. Guillen, however, contended there would be less strain on his troublesome left groin if he played right field instead of Mark Teahen.
Guillen and Hillman discussed the matter. Guillen got his wish; he was in right field and Teahen in left.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.