Astros All-Star right-hander Gerrit Cole, the biggest free-agent pitcher on the market this coming offseason, is scheduled to start for the Astros against the White Sox on Tuesday at Guaranteed Rate Field.

Imagine Cole on that same mound but in a Sox uniform next season, surrounded in a rotation by Sox All-Star Lucas Giolito, the revived Reynaldo Lopez, prized rookie Dylan Cease and the recovering (from Tommy John surgeries) Michael Kopech and Carlos Rodon.

Talk about the perfect fit. Cole, 28, could be the accomplished, premium finishing piece to take the rotation from Point B to Point A.

Without making a significant addition, the rotation “in the future can be one of the most dominant,” Giolito said after striking out 13 Athletics in a 2-0 loss Sunday.

Perhaps. Most of that assessment is based on potential, and the Sox likely will sign or trade for a proven starter to add to it, but it’s just not the Sox’ way to lavish huge long-term money on pitchers. Cole could command a minimum of five years in the market and at least $200 million.

“One thing is for certain, the competition for Cole will be huge,” an American League source said. “The White Sox actually signing Cole? Don’t see it.”

In other words, dream on if you’re a Sox fan.

Granted, the Sox were in the free-agent mix for Manny Machado and, to a lesser degree, Bryce Harper last offseason. But they were not willing to make a large-enough financial commitment to reel them in, and Machado took more guaranteed millions from the Padres. The biggest contract the Sox have ever given was to Jose Abreu at $68 million, and that was almost six years ago.

The 2020 season will be the fourth season of the rebuild and an important one. After two painful seasons, which were expected even at 95 and 100 losses, 2019 was turning a nice, necessary corner on the field only to lose steam after the All-Star break. Meanwhile, a farm system, albeit strong with prospects such as Luis Robert and Nick Madrigal at the top, isn’t boasting enough depth, a necessary commodity for protection against injuries and for executing trades for proven players when the time is right, and the time should be about now.

Just where are the Sox now? Still a long ways from the Astros.

Before his team’s scheduled game against them was rained out Monday, Sox manager Rick Renteria fielded several questions about the Astros, whose rebuild produced a World Series title in 2017 with more in sight.

“Every time we play really well-equipped clubs, you use it as a measuring stick because you have to,” Renteria said. “You want to be realistic in terms of assessing where you’re at and what it’s going to take to compete and win. They’re one of the best clubs in baseball, so playing against them and seeing how we fare is certainly something that we look forward to doing and having some positive outcomes.”

Without Cole, or a prime addition, Renteria described the Sox’ rotation picture as such:

“We have the makings, in terms of the men we have with us here and the guys that are going to be coming soon, of having a really solid rotation at the major-league level. And not just solid, I mean guys that potentially could be No. 1, 2, 3 type guys. We’ve said that since the beginning.

“You have a chance to have a really good rotation.”

Having a chance to have a great rotation would be better for a team with aspirations of contending for multiple championships but is nowhere near that. Being thought of as a destination for top talent and having a chance to land the Gerrit Coles of the world is going to be a necessary step.