"I think we'll end up making a deal or two," Wren said before Monday's game against the Indians at Chain of Lakes Park. "I'm not sure of the magnitude yet."
Whatever trade Wren potentially makes before the end of this week, it likely won't be one that dramatically changes the National League's balance of power.
But the Braves are hopeful it will be one of those under-the-radar trades that proves as valuable as the deal completed three years ago when they brought Jorge Sosa to Atlanta in exchange for Nick Green.
At the time, Green was out of Minor League options and expendable on the Braves roster. By trading him to the Rays, the Braves gained Sosa in time to benefit from his career-best 13-win season.
The out-of-option players who could draw the most trade interest for the Braves are right-handed relievers Chris Resop, Tyler Yates and Blaine Boyer; catcher Brayan Pena and first baseman Scott Thorman.
With fastballs that have been clocked in the range of 95 mph, each of the three relievers are of the live-arm variety other teams would covet on the waiver wire or possibly in the trade market.
As for Pena, his offensive talents as a switch-hitting catcher who has the ability to play the corner positions in the infield and outfield would also make him desirable to other organizations.
"At the end of the day, we're going to take the best player for our club and we're going to trade the other," Wren said. "We're not going to see who has the best market out there, make the trade and then keep the other guy. We're going to keep the best guy for us."
If one of these out-of-options players doesn't make the Opening Day roster, they would have to pass through waivers before being sent to the Minors.
The task assumed by Wren and manager Bobby Cox this week is to put the best talent on the 25-man roster and do whatever they can to prevent losing any of the remaining players to another team without compensation via the waiver wire.
"We've taken that position for the last couple of weeks," Wren said. "We started focusing on who the final 25 [players] to make sure we looked at the market for the other guys. So we're well along in that process."
As Wren evaluates his trade options, he's hoping to find a power source to improve his bench with a power source or veteran pinch-hitter.
One of the closest position battles in camp is being staged between Gregor Blanco and Josh Anderson, who are both bidding for the fourth outfield spot. But because both of these players have options, there isn't as much consequence surrounding which of them wins the battle, since the other can be sent to the Minors.
As for the competition in the bullpen, it looks like there might be two available spots. The only five relievers seemingly assured roster spots are closer Rafael Soriano, Peter Moylan, Manny Acosta, Jeff Bennett and left-hander Will Ohman.
If the Braves want another left-hander, they may opt to go with Royce Ring, who is also out of options and could be coveted by another organization that wants a left-handed specialist. But there's also a chance he could pass through waivers.
Although Yates has been a regular in the Braves bullpen for the past 1 1/2 seasons, Boyer, who has a 2.25 ERA in seven spring games, and Resop, who has 10 strikeouts and just one walk in 10 innings, seem to be ahead in the battle for the final bullpen spot.
Even after registering two strikeouts in a perfect ninth against the Indians on Monday afternoon, Yates didn't generate a lot of excitement. This might stem from the fact that he's walked 10 and surrendered seven hits in seven innings.
With Corky Miller seemingly the choice to be the backup catcher, Pena offers the Braves a predicament. While he could prove to be a consistent switch-hitter, he doesn't provide enough defensively to carry him as a utility player for an extended period.
Thorman, who has hit just .140 in his 43 at-bats this spring, also finds himself wondering if his days in the Braves' organization are numbered. While serving as the regular first baseman until Mark Teixeira was acquired last year, he struggled offensively and defensively.
There are certainly teams that could be interested in Thorman's power potential. But there's a chance the Braves could assume Teixeira will play almost every game and plan to use either Pena or Joe Borchard, who would provide the bench with power potential, as his occasional backup.
Needless to say, it's a stressful stretch for a number of these Braves players. But Thorman is attempting to prevent it from affecting how he plays during the always-important final week of the exhibition season.
"Whatever is going to happen is going to happen whether I worry about it or not," Thorman said.
Mark Bowman is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.