Valentine, who led the Mets to the World Series against the Yankees in 2000, will be the second managerial finalist to have a sit-down interview with the Indians. Former Washington manager Manny Acta met with Cleveland's owners and other front-office personnel on Tuesday.
Valentine, 59, spent the past six years managing the Chiba Lotte Marines in Japan. He's currently working as an analyst for ESPN. He managed Texas from 1985-92 and was with the Mets from 1996-2002.
The Indians will also interview Torey Lovullo, their Triple-A manager in Columbus on Friday, and intend to interview Los Angeles Dodgers batting coach Don Mattingly. General manager Mark Shapiro said he is considering interviews with two other undisclosed candidates.
As much as the Indians would like to sign a manager of Valentine's caliber, money could be an issue.
Valentine made nearly $4 million per season for Chiba Lotte, leading the team to the Japan Series championship in 2005. The club couldn't afford to keep him and management did not renew his contract despite an outpouring of support from fans, who held nightly vigils outside Chiba Marine Stadium and gathered more than 100,000 signatures on petitions to keep Valentine.
The Indians still owe former manager Eric Wedge $1.3 million for next season.
Ideally, Shapiro would like to have a new manager in place by the end of the World Series but said he's willing to wait longer for the right manager.
That could be the energetic Valentine, who has a career record of 1,117-1,072, and a longer track record than any of the other known candidates. He stayed current on major league baseball while managing in Japan and his hiring would probably be more popular with Cleveland fans now that former Indians manager Mike Hargrove and Travis Fryman are out of the mix.
Valentine posted four winning seasons and went 581-605 in Texas, but never got the Rangers to the playoffs. With the Mets, he was 536-467 and took them to the 2000 Subway Series, which they lost in five games.
Valentine was the Los Angeles Dodgers' No. 1 draft pick in 1968. He played parts of 10 seasons with the Dodgers, Anaheim, San Diego, the Mets and Seattle.