Kotsay was scratched from the Braves' starting lineup on Tuesday, as Boston and Atlanta tried to complete a deal.
ESPN.com -- citing sources -- reported that the Red Sox are "on the verge" of landing Kotsay in a trade.
Though no deal had been completed as of late Tuesday night, Kotsay seemed excited about the possibility.
"As a player, you want to win and have a chance to compete in the postseason," Kotsay said. "If I'm traded to a club that is in postseason position, that will be great. I've had fun [in Atlanta]. It's been great to play for Bobby [Cox] and be in this clubhouse."
Prior to Tuesday night's game, Drew (herniated disc) was placed on the 15-day disabled list, retroactive to Aug. 18.
Kotsay is hitting .289 with six homers, 37 RBIs in 318 at-bats. He has the ability to play center field and right field.
With Drew out of the mix, Coco Crisp has been starting in center field, with Jacoby Ellsbury taking over in right.
Even before Drew went down, the Red Sox were seeking additional depth in the outfield. They had a waiver deal worked out with the Padres for Brian Giles on Aug. 8, but that fell through when Giles exercised his no-trade clause.
The 32-year-old Kotsay has a limited no-trade clause, but that doesn't figure to be any kind of issue this time around. In fact, Kotsay said he wasn't even sure if the Red Sox were one of the teams on his no-trade list.
Kotsay is a .282 career hitter with 109 homers and 597 RBIs. Aside from being a professional hitter, Kotsay has always been an above-average outfielder.
Playing in his 12th Major League season, Kotsay has been on just one playoff team -- the 2006 Oakland Athletics.
Epstein has certainly been aggressive on the trade market this season. On July 31, he traded superstar Manny Ramirez to the Dodgers while landing Jason Bay from the Pirates. Epstein acquired veteran right-hander Paul Byrd from the Indians for cash considerations on Aug. 12.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.