(CBS) The recent elimination of the Tampa Bay Rays could mean big things for the Chicago White Sox.

On the South Side, a name near the top of the list for Ozzie Guillen successors has been Dave Martinez, the current bench coach of the Rays. Martinez, 47, has both played in the White Sox organization for owner Jerry Reinsdorf and as a teammate of general manager Kenny Williams in Montreal.

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‘‘I’m overwhelmed by the fact that they’re considering me as a managerial candidate,’’ Martinez told the Chicago Sun-Times before the start of the Rays’ final game of the season Tuesday. ‘‘At the end of all this, I’d love to sit down with Kenny and talk about it. . . . But right now, my focus is on what’s going on here and trying to win today.’’

The connections between Martinez and the White Sox are strong, and with the Rays being eliminated from the playoffs, if he’s the guy at the top of William’s “short list,” a decision could come soon.

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This isn’t the first time Martinez has been considered for a managing position as he was interviewed by Toronto and Cleveland for their vacant positions over the past two seasons.

Still, a chance to return to Chicago could be tempting for Martinez.

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‘‘It’s a great city,’’ he said, ‘‘one of my favorite places.’’