Fort Myers Miracle manger Doug Mientkiewicz talked with his players before Tuesday night game with the Tampa Bay Yankees June 2, 2014 in Fort Myers , Florida (Brian Stensaas — DML - Star Tribune Star Tribune/The Minnesota Star Tribune)

Twins General Manager Terry Ryan is pushing on with his search for a new manager, interviewing former Twins first baseman Doug Mientkiewicz for the job Thursday, according to a person with knowledge of the search process.

Ryan on Thursday headed to Fort Myers, Fla., to watch prospects in the instructional league, so the interview is believed to have taken place there. Mientkiewicz, 40, just completed his second year as manager at Class A Fort Myers, leading the Twins affiliate to the Florida State League title.

Paul Molitor, considered the favorite to replace the fired Ron Gardenhire, interviewed Wednesday. Molitor and Mientkiewicz are the only known candidates to have interviewed. Two other potential in-house candidates, bench coach Terry Steinbach and Class AAA Rochester manager Gene Glynn, have not yet been contacted but would like a chance to throw their hats into the ring.

Before leaving, Ryan said he has already interviewed several candidates for the position — declining to reveal whom — and planned to continue interviews in Florida.

"There is plenty of interest in this job," Ryan said.

Mientkiewicz told the Star Tribune on Tuesday that he would be interested if contacted.

"Everybody wants to be a big-league manager, that's pretty much where it's at," Mientkiewicz said, "but there are a lot smarter people than me making decisions. Of course I would listen to Terry."

Mientkiewicz spent 6½ of his 12 major league seasons with the Twins, debuting in 1998 and becoming part of the group of players who pulled the Twins from years of losing to win three consecutive American League Central titles from 2002 to 2004. During the 2004 season, he was traded to Boston, helping the Red Sox win the World Series that year.

Mientkiewicz frequently credits Tom Kelly and Gardenhire for shaping him as a player, and came back to manage in the Twins organization to mold players like he was.

"I just want the best for this organization," he said, "and the best man for the job to get this thing back to where it should be."

Steinbach just finished his second season with the club but, like the rest of the coaching staff, his status is in limbo until the managerial search is over.

"Absolutely, I would like to sit down with [Ryan] if he wants to do that," Steinbach said.

Glynn just finished his third season managing Rochester, going 77-67 in each of the past two seasons. Saturday, Glynn will leave to be Henry Blanco's bench coach for Margarita of the Venezuela winter league, but he would fly back if the Twins wanted to interview him.

"I'm hoping to," Glynn said. "Maybe it will happen."

In addition to assembling his own list, Ryan is receiving numerous calls from people hoping for an interview. He said he hasn't been surprised by any of the calls.

"I think this is an attractive job," he said. "Anyone that has aspirations of being a major league manager, especially guys who have never had a chance, this should be a pretty good thing."

The Twins wrap up instructional league Tuesday, and then 75 to 80 club employees will head to Fort Myers on Oct. 12 for six days of organizational meetings. The next big dates on the offseason calendar are the annual general manager's meetings Nov. 9-12 in Phoenix. Ryan, with help from assistant GM Rob Antony, will have to conduct the search around these important dates.

Some fans, wanting to see a different voice, have clamored for someone outside the organization to take over. So far, the two interviews that Ryan has been known to have had have been in-house candidates.

Ryan chuckled when asked about hiring outside of the organization.

"People are going to have views on who it should and should not be," he said. "Hopefully we'll do a good job here and get the right person.''