(CBS) A key part of the White Sox’s rebuilding plan is to sign 19-year-old Cuban outfielder Luis Robert, 670 The Score’s Bruce Levine reported in April.

Now with the Robert sweepstakes underway, the White Sox are one of the favorites to land him — and perhaps the favorite. The White Sox are one of the teams with the most international money to spend prior to the June 15 deadline.

“Obviously the White Sox are one of the teams involved,” MLB Network contributor and Fanrag Sports columnist Jon Heyman said on the Mully and Hanley Show on Monday morning. “I’ve heard St. Louis, Houston, about eight other teams. It sounds like Atlanta has bowed out at this point. But he’s an extremely talented outfielder and just a kind of guy the White Sox could use.”

After initially saying he wouldn’t be surprised to see Robert sign with the White Sox, Heyman went a little further in evaluating the situation.

“The White Sox are a big-market team, need help particularly in the outfield perhaps — although the Garcias are playing well,” Heyman said. “I think he fits. They seem to like him. They’ve talked about him a little bit. At this point, it’d be a surprise if he went somewhere else.”

Robert can sign as early as this weekend.

“The timing, I’m not sure,” Heyman said. “I have heard they’re going to get more than $20 million or at least that’s what (his camp) is telling teams, which kind of jibes with what we heard a month ago, which was that they had $25 million in the pocket. At that point, teams weren’t really supposed to be negotiating, but you know how this goes.”

Listen to Heyman’s full interview below. He also talks about the Cubs’ recent woes.

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