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LOS ANGELES (CBS) – The Los Angeles Dodgers and Chicago Cubs appear to be close on a trade involving pitcher Ryan Dempster.

ESPNChicago.com is reporting the Dodgers have made the Cubs a proposal and Chicago is preparing to have replacements ready to fill their roster for their weekend series in St. Louis.

The Cubs have indicted a strong desire for acquiring young pitching, but Ken Rosenthal of Fox Sports Tweets, the Dodgers are not including top-prospect Zach Lee in an offer.

Dempster, 35, has a 1.86 ERA this season, the best in the baseball and has pitched 33 consecutive scoreless innings.

Orel Hershiser has the MLB record, with 59.2 scoreless innings with the Dodgers in 1988.

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