White Sox GM Rick Hahn might have tough decisions to make at trade deadline

It’s easy to fall in love with your guys when they are making you look smart as a general manager, but the White Sox’ Rick Hahn knows he’ll have to break up with closer Alex Colome and/or catcher James McCann if someone makes an offer he can’t refuse.

Hahn didn’t bat 1.000 this past offseason, but he did connect when he acquired Colome (13-for-13 in save opportunities) from the Mariners for catcher Omar Narvaez and when he signed McCann (.329 batting average) for $2.5 million as a free agent. McCann is second among American League catchers in All-Star voting.

Teams interested in those two, who are subject to arbitration for another season, could be filling up Hahn’s phone with calls and texts. Colome would be in the highest demand because contenders almost always want more bullpen help.

Then again, the Sox are in the third season of their rebuild, not the first. They are three games below .500 at 31-34 after their 12-1 loss to the Nationals, not 19 under like they were a year ago.

‘‘That’s an interesting question,’’ Hahn said. ‘‘Perhaps a tricky one here over the next few weeks. We are going to have guys who other teams want. From our standpoint, it’s always going to be about putting us in the best long-term position. We haven’t quite pivoted to that strictly win-now, short-term focus.’’

Whether to keep Colome and McCann or trade them will depend on how badly they’re wanted elsewhere. Opponents are 2-for-42 with two walks in save situations against Colome. And in addition to his batting average, McCann has received thumbs-up reviews from Sox pitchers for pitch-calling and is a good guy in the clubhouse. These are guys the Sox can win with next season.

‘‘When you are talking about guys who could potentially play a role on the 2020 White Sox, a year we expect to take yet another step forward in the process and start being in the mix for playing in October, the calculus becomes a little more heavily weighted in terms of keeping a guy,’’ Hahn said. ‘‘In the end, this will be about market value. It’s going to be about demand for our players and what they are able to potentially bring back, then balancing that off against the value they have to us in a White Sox uniform in 2020.’’

There would be demand for shortstop Tim Anderson, third baseman Yoan Moncada, rookie outfielder Eloy Jimenez, right-handers Lucas Giolito and Reynaldo Lopez and left-hander Aaron Bummer, too, but they are key pieces of the Sox’ core and aren’t going anywhere.

Leury Garcia, who entered Monday batting .281/.318/.348 as an everyday player who can play multiple positions, has two more seasons of club control. Then there’s first baseman Jose Abreu, who is in the final season of his contract. That automatically makes him tradable, but Hahn has suggested more than a passing desire to bring him back.

Major League Baseball has abolished August trades, switching to one non-waiver deadline July 31. That might get trade talks moving sooner than usual.

‘‘Because of the removal of August trades, you are going to probably see more activity earlier than you’ve had in the past,’’ Hahn said. ‘‘Not only do teams have to pick a lane in terms of whether they are buyers or sellers, the sellers basically have to get their work done sooner rather than later. It will be interesting to see how it plays out over the course of the next five or six weeks, with more activity starting up right around the All-Star break.’’