White Sox preparing to go shopping

MINNEAPOLIS — When Rockies shortstop Trevor Story’s name is added to the intriguing list of possibilities for the White Sox leading up to the trade deadline July 30 — a list that already includes Diamondbacks infielder Eduardo Escobar and Pirates second baseman Adam Frazier — heads will turn.

For the most part, Sox players are keeping their heads down and not stressing out about who might or might not join them for the second half. By the same token, they are as intrigued as fans are.

‘‘I’m too old to play GM,’’ catcher Yasmani Grandal said. ‘‘I trust the front office and what they’re doing. If they decide to make a move, great. If not, we’re going to concentrate on what we have now. And when the move comes — if it comes — we’ll concentrate on that.’’

The Sox, who took a six-game lead in the American League Central into their game Monday against the Twins, already have used most of their 40-man roster. The players expect the front office to make upgrades.

‘‘Oh, yeah,’’ right-hander Lucas Giolito told the Sun-Times. ‘‘I’ve been reading certain things and have had certain conversations with some guys in the front office.

‘‘That’s what I enjoy about our front office: They are very open to suggestions, to talking to players and hearing what we think. I’m not going to name names, but we can definitely use some help in certain areas.’’

Story, a two-time All-Star with the Rockies who is in the last year of his contract, presumably would play second base if a deal is made. The Sox wouldn’t ask shortstop Tim Anderson to move, especially for a rental player.

The Sox are weighing which prospects they would be willing to part with, knowing selling teams can wait for the best offer. With almost a month before the deadline, neither side is under the gun to pull the trigger on a deal now.

The Sox probably have enough on their roster to win their division despite a slew of injuries. But they are all but certain to add at least one proven reliever, and second base has been missing an impact bat since Nick Madrigal went down with a season-ending hamstring injury.

It’s all about being fortified for October.

‘‘It’s kind of hard not to think about it and talk about it, right?’’ Grandal said. ‘‘We talk about other teams and the moves they can possibly make and the people they need, but I don’t think I’ve heard too many guys talk about what we need because we trust in the guys on the 40-man roster who can come up and do their job.’’

Because of major injuries to Eloy Jimenez and Luis Robert and minor injuries to others, the Sox have started 12 outfielders this season, including Triple-A call-ups Brian Goodwin, Billy Hamilton, Gavin Sheets, Nick Williams and Luis Gonzalez and converted corner infielders Andrew Vaughn and Jake Lamb.

‘‘The front office and coaching staff — the whole organization — have done a great job preparing the guys in the minor leagues on the 40-man roster to be successful in the big leagues,’’ Grandal said. ‘‘We count on all those guys to come up and do their job.

‘‘Hopefully [Jimenez and Robert] come back, but we don’t want to push those guys too much. Those are injuries that are pretty big. Would they be a huge help? Obviously. Hopefully during the last stretch we see an appearance from them, and they can help us make a huge run to finish the year out into the playoffs.’’

Those are still unknowns, however. And even if they were sure things, the front office would be expected to be aggressive. The Sox’ chance to win is now.

‘‘We don’t want to win any more than they want to win,’’ manager Tony La Russa said of the front office. ‘‘That is real clear to all of us in uniform. They sweat and bleed and celebrate like we do. [A trade has] got to be reasonable. If there is a reasonable move out there, we’re confident they’ll make it.’’