Mulder, 6-foot-6 and 215 pounds, is on the comeback trail after missing 2009 because of shoulder surgery. The Royals would like to bring a left-handed starter into their all-right-handed rotation.
Royals general manager Dayton Moore acknowledged on Wednesday that the Royals have interest in the two-time American League All-Star.
Mulder posted a 21-8 record for the A's in 2001 with a 3.48 ERA and was named to the All-Star teams in 2003-04. He was in the AL playoffs with Oakland in 2001-02 and in the National League playoffs with the St. Cardinals in '05.
But he hasn't pitched a full season in the Majors since then.
"Last year and the year before, he was trying to do something," Moore said. "I think he'll try to come back and pitch. He went through the rehab process, I think two years ago, and he just couldn't quite make it back. Some guys push it too fast."
The Brewers also have interest in Mulder. They could have an edge because of Mulder's relationship with the Brewers' new pitching coach, Rick Peterson. He worked with Mulder when both were with the A's.
"We'll go through the process like everybody else," Moore said. "I'm sure it'll be a low-base, incentive-type deal predicated on him making the team or getting to the Major Leagues, so we'll see."
Mulder has a Major League career record of 103-60 and a 4.18 ERA in 205 games, all but two of them starts. But he missed all of last season.
"In deals like that, players [sometimes] choose the opportunity where they can progress at a slower pace," Moore said. "Maybe our situation's right, maybe it's not for those types of players. You just evaluate them as they come."
The Royals' search for a catcher yielded nothing new Wednesday.
"In that particular market, things are moving slow, which leads me to believe that the clubs that are seeking players that we're seeking are all consistent with their approaches and nobody's really winning the negotiations," Moore said. "Everybody's probably pretty similar."
Kansas City is reportedly looking at, among others, free agents Rod Barajas, Jason Kendall and Jose Molina.
There was a report on Wednesday night that the Royals had offered Kendall a two-year contract, but Moore declined to comment.
"I can't comment on people that we've offered contracts or haven't offered contracts to," Moore said. "Someone told me that, too, but I just can't say anything about that."
Nor was there any progress on a center fielder or pitchers. By late Wednesday afternoon, the Royals had made no deals at the Winter Meetings, which close Thursday.
"It's unpredictable," Moore said. "I wouldn't be surprised if we got something done or if we didn't get something done and two weeks from now, we're in the same boat. It's just unpredictable."
The Rule 5 Draft comes at 8 a.m. CT on Thursday, and the Royals have the fourth choice. But they'd have to clear a spot on their 40-man roster to use it.
Just before the Winter Meetings began, the Royals agreed to spend about $7 million on Cuban left-hander Noel Arguelles. Next week in Houston, another highly-regarded lefty from Cuba, Aroldis Chapman, will have a showcase event in Houston for Major League clubs.
Moore indicated the Royals would take a look. Chapman, however, has been rumored to be looking at a signing bonus of $15 million or more.
"I don't know," Moore said. "Arguelles was rumored at $14 million at one time, so you don't know. You just do the work."
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.