By Bruce Levine–

CHICAGO (CBS) — Over the next two-and-a-half-months ahead of the July 31 non-waiver trade deadline, the White Sox should be one of the most active teams in trade discussions.

READ MORE: Chicago Radio Sportscaster Les Grobstein Dead At 69

After the amateur draft that begins June 12 is completed, executives will get serious in exploring the way to improve their chances of making the playoffs and competing for a championship. Already, top scouts from contending teams — including the Red Sox, Yankees, Nationals and Pirates — are in Chicago this week to look at the White Sox’s top available trade chips as they’ve embarked on a rebuild.

The current perception is the White Sox will trade any player on their big league roster now besides 23-year-old shortstop Tim Anderson. Most notably, left-hander Jose Quintana and closer David Robertson are on the market.

“They have players that can help a lot of clubs be better,” said a National League talent evaluator watching the White Sox on this homestand. “You start with Jose Quintana and move quickly to David Robertson. These are difference-makers when it comes to a pennant race. Both pitchers will get dealt, and the White Sox should get some interesting young players in return.”

READ MORE: Family Of Amazon Delivery Driver Killed When Tornado Hit Downstate Warehouse To File Lawsuit

The White Sox haven’t made a trade this year. Their two big moves came a day apart last December, when at the Winter Meetings they dealt ace left-hander Chris Sale to the Red Sox and outfielder Adam Eaton to the Nationals in deals that netted them seven quality young prospects. Since that time, Chicago has been willing to deal but hasn’t found anything to its liking.

“I have been in contact with some clubs,” general manager Rick Hahn said Tuesday. “After the draft in June, you can expect more conversations to pick up. Until that time, clubs are looking at the amateur draft and international signings.”

Hahn on Tuesday was also asked about the chance of having the Cubs as trading partners. The sentiment has been that the two clubs wouldn’t trade due to their geographical proximity and the scrutiny that comes with sharing a city. Hahn emphasized that he absolutely wouldn’t eliminate the Cubs as a trade partner.

“I have heard this a lot, and I am sure I will have to go over this a lot over the next several years,” he said. “Any deal we make is about maximizing the future of the White Sox. We will deal with all 29 clubs other clubs. I can point to our willingness to deal with teams in our own division. There is zero issue with doing a deal with the Cubs or any of the other 28 teams. Hopefully, when we make a trade, both teams end up winners.”

MORE NEWS: 2 Men Shot While Sitting In Car In Humboldt Park

Bruce Levine covers the Cubs and White Sox for 670 The Score and Follow him on Twitter @MLBBruceLevine.