A source told ESPN.com's Jayson Stark that the Red Sox would attempt to move newly acquired Adam LaRoche either to a third team or in a companion deal to make room for Martinez in their lineup.
The Red Sox have been working on parallel deals with Toronto for Roy Halladay, San Diego for Adrian Gonzalez and Cleveland for Martinez, the site said. Additionally, there were indications that the Red Sox were not making progress with Toronto and San Diego, and they were having trouble making the pieces fit with Cleveland.
Boston is contacting other teams to help make the deal fit and is believed to be searching for a third team.
The report states one potential reason for involving a third club was the need to find a destination for LaRoche, but there are very few contending teams searching for a first baseman.
Tampa Bay is another possible destination for Martinez. Cleveland was heavily scouting the Rays' Minor League system, and the Indians had multiple scouts watching the Rays' Triple-A Durham team.
According to the report, the Rays don't seem to have the financial flexibility to absorb Martinez's contract this year without subtracting a player like Scott Kazmir at the same time.
One source told ESPN.com that it was a long shot for the Rays to pull off two deals of that size.
Jesse Sanchez is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.