The Boston Red Sox have made an offer to free agent pitcher Edwin Jackson, but have likely been outbid by other teams vying for his services, ESPN's Gordon Edes reports.

A league source told Edes that Boston's offer to Jackson -- reportedly between $5 million and $6 million for one season -- is not competitive with other offers Jackson has already received. The right-handed starter, who is viewed as perhaps the top pitcher left on the market, has noted that he would like a multi-year deal.

The Red Sox are also expected to be out of the running in the Roy Oswalt sweepstakes. Oswalt, another highly-regarded starter to whom the Red Sox recently made an offer, is said to prefer the St. Louis Cardinals or Texas Rangers.

Boston is set at the top of its rotation with Jon Lester, Josh Beckett and Clay Buchholz, but question marks still loom in the rotation's back end.

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