#1: A prospect-based proposal
This is probably the most likely of the three packages if a deal were to be made. The White Sox probably won’t be too willing to part with a young player with major league experience or a top prospect, so this is the only possible deal in which both criteria are met.
First, the White Sox would be parting with two top-100 prospects, and their No. 9 and No. 10 ranked prospects, both of which have been top-100 prospects at one point.
The headliner in this deal would be Dane Dunning. Acquired in 2016 from the Washington Nationals, Dunning is the highest-ranking prospect in this deal. The righty is a perennial top-100 prospect, and is close to being ready for the majors. A polished, consistent righty, Dunning is a safe bet to pan out at the major league level.
The second piece of the deal would be Blake Rutherford. Another top-100 prospect, Rutherford is a toolsy outfielder that could fit anywhere in the Mets future outfield. A 2016 first-rounder, Rutherford possess major upside and 20-20 potential.
The final two pieces of the deal would be Luis Basabe and Alec Hansen. Basabe, who was acquired from the Boston Red Sox back in 2016, is a high-ceiling, low-floor outfielder, who is coming off of a great 2018 season in which he was selected to the 2018 All-Star Futures Game. Secondly, Alec Hansen, a 2016 second-rounder, led the Minors in strikeouts in 2017 before imploding in 2018. Hansen has a really high upside, and would be a gamble as the final piece.