BOSTON — On the eve of the non-waiver trade deadline, the Red Sox last night found themselves stonewalled in their search for a right-handed-hitting outfielder and experienced bullpen help, leaving open the possibility that the team will, for the second straight summer, be inactive during baseball’s busiest in-season swap meet.

This morning, the Red Sox did announce that they had traded pitcher Joel Pineiro, who was starting in Pawtucket after failing to catch on in the Boston bullpen and being designated for assignment, to the St. Louis Cardinals for a player to be named later and cash.

The Sox remained in discussions with the Chicago White Sox yesterday concerning outfielder Jermaine Dye, the team’s top priority when it comes to upgrading its offense.

The White Sox demanded the Red Sox include either reliever Manny Delcarmen or Double-A pitching prospect Justin Masterson as part of a package for Dye, but the Sox balked at both requests.

Delcarmen, though he had two poor outings in the last week, figures heavily in the team’s bullpen plans for the final two months, particularly in light of the recurring shoulder issues plaguing veteran Mike Timlin. Masterson, though not valued as highly as fellow prospect Clay Buchholz, is nonetheless considered virtually untouchable — especially for a short-term rental like Dye, who can be a free agent after this season.

The 33-year-old Dye has a no-trade clause in his contract and initially rebuffed the Red Sox, feeling that he wouldn’t get enough playing time to bolster his value entering the free-agent market.

But the Sox sought to allay those fears, reportedly assuring Dye that he would play five times per week, presumably at the expense of fellow outfielder J.D. Drew, whose production has been a huge disappointment in the first year of a five-year deal in Boston.

Chicago’s options for Dye would seem limited, with the Angels and Dodgers, two potential trade partners, showing far less interest of late. Still, the Red Sox haven’t been able to meet the White Sox’ demands, and last night there existed the possibility that Chicago would perhaps continue to solicit offers for Dye into August, when players can be dealt only after first clearing waivers.

The Sox are willing to move Wily Mo Pena and other young pitchers — including Kason Gabbard or Craig Hansen.

Dye, who has had a hot July (8 homers, 19 RBI), could platoon with Drew and also offer insurance at DH. David Ortiz has yet to hit a homer off a lefty all season and has seen his power numbers greatly reduced by a balky knee.

The Sox continue to show an interest in reliever Eric Gagne of the Texas Rangers, but there are two complications at work.

First, the Sox are not on Gagne’s list of 12 approved teams, meaning the Red Sox would have to satisfy the reliever’s contractual demands. In all likelihood, that would include Gagne asking that the Sox pay the remainder of his remaining incentive bonus ($3.65 million) for games finished.

(Gagne would set up Jonathan Papelbon for the Sox, and not close, thus depriving him of the opportunity to finish games and earn the incentive money.)

Then, the Sox would have to meet the Rangers’ asking price, which remains high. A major-league source said yesterday that in addition to the Sox, the Yankees and New York Mets are the teams most interested in obtaining Gagne.

For the last few days, the Rangers were more consumed with finding the best deal for first baseman Mark Teixeira. Now that Teixeria is headed to Atlanta as part of a six-player deal, Texas GM Jon Daniels can presumably focus more on a trade for Gagne before the deadline arrives at 4 p.m. today.

A limited number of other relievers interest the Sox, including two Pirates: lefty Damaso Marte and righty Salomon Torres.

The Sox had also been monitoring Octavio Dotel, whom they discussed as a free agent last winter. But indications last night were that the Royals were going to deal Dotel to the Atlanta Braves for starter Kyle Davies.

Kansas City general manager Dayton Moore used to work for the Braves, and his knowledge of their system made a deal easier to consummate.

smcadam@projo.com