According to several sources the Red Sox made another offer to Chicago for OF Jermaine Dye.

The Sox also reportedly have made the best offer to Texas for closer Eric Gagne. Reportedly the Sox are willing to part with Triple A OF David Murphy and P Kason Gabbard.

Both Dye and Gagne have limited no trade clauses and both are concerned about how Boston would deploy them. Dye has a no-trade to four teams including Boston, while Gagne has the Sox listed among 12 teams on his list. Gagne has bonuses based on how many games hefinishes and has already made an additional $1.3 million on top of his $6 million salary. But coming to Boston to set up closer Jonathan Papelbon would give him other opportunities such as playoff and World Series shares and the ability to showcase himself for a big free agency pay out for 2008. Word is Theo and the Trio maybe willing to just pay out Gagne’s $5 million in bonuses in order to lure him to Beantown.

Gordon Edes of the Boston Globe is reporting that the Rangers now may prefer to hold onto Gagne and try to sign him to an extension.

Other teams interested in Gagne are the Brewers and the Yankees, both of whom have quality closers already in place. While the Sox are in competition with the Angels, Diamondbacks and Dodgers for Dye.

A couple of MLB GM’s who have info on the potential deals said the Red Sox would not discuss the possibility of trading Manny Delcarmen, Jon Lester or Michael Bowden. They also remained adamant in not trading Clay Buchholtz, Jacoby Ellsbury or Justin Masterson.

The Sox are still working hard to move OF Wily Mo Pena, Pawtucket pitcher Devern Hansack and fifth starter Kason Gabbard has drawn considerable interest as well.