Bourn, who hit .274 with 42 stolen bases, had an $6,845,000 base salary this season and earned a $50,000 bonus for making the NL All-Star team.
Wren said he'll be a serious offseason shopper.
"We're going to be looking for premium players, I think there's no doubt about that," he said. "We're losing one Hall of Fame player and the salary that goes with that Hall of Fame player, and we're going to be looking to replace him. And as we do that, it gives us the opportunity to add another big player."
Atlanta's moves could come in in trades.
"There are not a lot of pieces out there in the free-agent market this year that are all that appealing," Wren said. "We may have to look other places."
Left fielder Martin Prado and Juan Francisco are possible replacements for Jones. Prado, a former All-Star second baseman, backed up Jones at third base and even filled in at shortstop this season.
Francisco hit .234 with nine homers in 192 at-bats. He could provide more power than Prado, a stronger defensive player who hit .301 with 10 homers, 70 RBIs and 17 steals.
Wren said the "ideal position" for Prado would be in the infield, but he noted that would leave an opening in left.
"You don't necessarily get to go out on the market and get the perfect guy for your team," he said. "We'll have to see how that goes."
Atlanta is expected to exercise their 2013 club options on catcher Brian McCann ($12 million) and right-hander Tim Hudson ($9 million).
Wren said the Braves have a "dynamic young core" of players, including right fielder Jason Heyward, first baseman Freddie Freeman and shortstop Andrelton Simmons.
Their rotation was bolstered by left-hander Mike Minor's strong second half and the emergence of Kris Medlen. Closer Craig Kimbrel heads a strong bullpen.
"Our bullpen is intact," Wren said. "Our starting rotation is intact. There are a lot of things that are real positive going into next year, and I think guys are going to get better. I'm very, very optimistic about where we sit as a franchise with the thought of adding a couple of key pieces."