They would have had plenty of time to discuss it, though. The two were teammates in the New York Yankees' farm system, playing together across three different levels that year.
Now, with Andrew Bailey out until after the All-Star break, either Aceves or Melancon is likely to take over the ninth inning for Boston. (General manager Ben Cherington said Daniel Bard will remain in the rotation.)
Both had breakout campaigns in 2011. Aceves excelled at pitching in a pennant race in a big market, but there's reason to believe he won't be able to repeat it. Melancon did all his damage on a last-place team, but the advanced stats support his effectiveness.
So who deserves to handle the most pressure-filled position on the team?
No one in the majors pitched more innings out of the bullpen than Aceves in 2011. And few pitched better than his 2.03 ERA and .193 opponent batting average as a reliever.
The last AL reliever with an ERA below 2.10 in at least 90 relief innings? Mariano Rivera in 1996, the season before he became a closer.
So why should the Red Sox proceed with caution if they are considering Aceves for the job?
As good as Aceves was in 2011, red flags indicate he might not be able to do it again.
Among Red Sox with at least 50 innings pitched, only Andrew Miller had a worse strikeout-to-walk ratio than Aceves' 1.90. Those numbers don't even include Aceves' 15 hit batsmen.
Without a big strikeout rate, Aceves relies heavily on the defense behind him. The league average for a ball put in play was .298 in 2011. Opponents had a .235 BABIP against Aceves, third-lowest among those who faced 400 batters.
In 2010, the top three in that category were Jamie Moyer (who didn't pitch in 2011), Trevor Cahill and Bronson Arroyo. Both Cahill and Arroyo saw a rise in ERA of over one run in 2011 as their BABIP normalized.
History is full of closers who get lucky with a low BABIP and then collapse the next season. This is even more common when that pitcher has a poor strikeout-to-walk ratio.
There have been 15 pitchers with 20 saves in a season in which they had a strikeout-to-walk ratio below 2.0 and a BABIP under .235. That list is full of closers who had seasons that are now considered flukes.
For some young pitchers (2006 Chris Ray, 1969 Ken Tatum) it set an impossible precedent they'd never replicate. Others (2008 Troy Percival, 1992 Steve Farr) enjoyed a final great season before reality set in.
Last season, Francisco Cordero fit those requirements. Despite 37 saves and a 2.45 ERA, he couldn't find a closer job this offseason. Sometimes the standard stats just don't tell the full story of how a pitcher performed.
A stat called xFIP -- or expected fielding independent pitching -- attempts to measure a pitcher's performance based on controllable outcomes. It also helps explain just how fortunate Aceves was in 2011.
His 2.61 ERA was better than Neftali Feliz, Jonathan Papelbon and several other established closers last season. Among pitchers with at least 100 innings, it ranked seventh in the majors. But his 4.77 xFIP ranked 141st out of 145. Instead of putting him among elite closers, it placed him among names like Clay Hensley and Andrew Miller.
These numbers don't diminish the season Aceves had in 2011. But they do provide caution in assuming it will happen again.
So what do those numbers say about Melancon's 2.78 ERA? He did that with a 3.14 xFIP and .286 BABIP. In other words, Melancon's breakout season was far more supported by his peripheral stats.
In his first full season in the majors, Melancon notched 20 saves. He even finished strong, with 11 straight scoreless outings to end the season.
So what's the concern?
It's not often that you find a closer who relies so much on a curveball.
Melancon threw 27.3 percent curves in 2011. According to FanGraphs, the last closer to throw curves at that high of a rate was Danny Graves (28.1 percent in 2002). Melancon threw the curve more than half the time in two-strike counts. That led to 38 strikeouts on curves, third-most among relievers.
The prototypical closer overpowers opponents, much the way Papelbon did. That's why Daniel Bard's triple-digit fastball remains a tempting option. Melancon's bread-and-butter pitch travels only 82 mph. That certainly makes his 92 mph fastball appear much faster.
But a closer doesn't have to be a strikeout pitcher. Part of Melancon's value is as a ground-ball pitcher. In 2011, his 57.9 ground-ball percentage was the highest among those with 20 saves.
The bigger concern remains that Melancon's success came in the low-pressure anonymity of Houston.
Not every inning is created equal. Aceves posted a 1.55 ERA over the final two months in the midst of a heated pennant race. Meanwhile, Melancon pitched for a team that finished 40 games back.
So will his curveball-throwing, groundball-inducing style work as a closer under the Boston spotlight?
The numbers say it's worth finding out.
Jeremy Lundblad is a senior researcher with ESPN Stats & Information. He provides statistical analysis for ESPNBoston.com.