On Wednesday morning, Jerry Crasnick of ESPN.com and Baseball America reported that the trade was in the "due diligence" phase, according to a source.
Team officials have not confirmed the reports.
Soler seemed to be the odd man out in the Cubs outfield with the return of Kyle Schwarber. In three seasons, Soler has batted .258 with 27 home runs and 98 RBIs. A right-handed hitter, he is entering the sixth year of a nine-year, $30 million contract. Leg injuries have limited Soler, who played 101 games in 2015, hitting .262.
This season, Davis was on the disabled list twice because of a right forearm strain and a right flexor strain.