The two teams reportedly discussed the deal before the trade deadline on July 31.
Jackson still has about $24 million left on his deal that runs through the 2016 season, and Upton is owed around $50 million of a $75.25 million contract through 2017.
Both players have struggled so far this year.
Jackson is 6-14 with a 6.09 ERA in 26 starts and 139 innings for Chicago, who are in last place in the National League Central.
Upton is batting .205 with nine home runs, 31 RBI and a .280 on-base percentage this season. He leads the major leagues in strikeouts.
- Scooby Axson