By Dan Bernstein–
CBSChicago.com senior columnist

(CBS) The dust has settled after the crosstown trade that caught Chicago baseball by surprise last Thursday, but both the Cubs and White Sox continue to work the phones to optimize their respective rosters. They have divergent goals to accomplish before the July 31 non-waiver deadline but are equally busy.

For Cubs president of baseball operations Theo Epstein, that means adding a useful arm for the bullpen that can matter in high-leverage situations and staying involved in conversations regarding starting pitching, as sources say they have been regarding Athletics right-hander Sonny Gray and others. Also on the Cubs’ wish list is a veteran catcher, ideally one who hits left-handed — a platoon preference of manager Joe Maddon at the position. Tigers catcher Alex Avila would be an obvious fit, but his outlier offensive season could be driving up the price. The 30-year-old Avila is slashing .292/.420/.518 for an OPS+ of 150, posting a 2.3 fWAR that’s the equal of Willson Contreras for the second-best number among all catchers behind Buster Posey’s 3.1. That Avila is known to be a strongly positive clubhouse presence is all the better, too, but nobody expected him to be this good right now.

As much as the Cubs like Victor Caratini, they’ve made it clear that they believe their newly bolstered and recovering pitching staff could benefit from a more experienced receiver involved now that both David Ross and Miguel Montero are gone.

White Sox general manager Rick Hahn is living in a vastly different world while trying to accelerate further his already rapid simultaneous teardown/stock-up, but the White Sox are reported to be open to selling off any of the older players who have now become vestigial organs left over from the go-for-it days. Closer David Robertson could go at any time the market seems right, and the same now applies to third baseman Todd Frazier, outfielders Melky Cabrera and other relievers like Tommy Kahnle, whose fastball has averaged an eye-popping 97.9 mph this year that makes it the 14th-hardest pitch in the game, per Statcast.

Jose Abreu might appear valuable with a slash-line of .294/.347/.513, but bat-only first basemen are relatively easy to find and don’t often command a premium in trade. His worth as a DH also cuts away half the suitors.

What the Jose Quintana deal did along with help both teams was enliven the possibility that the open line of communication could engender more discussions between the two that align with their differing timetables in a way that each side can continue to get closer to winning another World Series.

The meatball narrative vaporized. We now know that these are reasonable people looking to do good baseball business, and some of it may still be close to home for all concerned.

Dan Bernstein is a co-host of 670 The Score’s “Bernstein and Goff Show” in afternoon drive. You can follow him on Twitter  @dan_bernstein and read more of his columns here.