Teams must make their departing players a qualifying offer in order to be eligible for draft pick compensation if a player signs a major league contract elsewhere before the amateur draft in June.
Davis will almost certainly garner far more money from the free agent market. The 29-year-old led the majors with 47 home runs in 2015 and drove in 117 runs in 160 games.
Wieters has spent his entire career with Baltimore. The 29-year-old hit .267 with eight homers in an injury-shortened season.
Chen went 11-8 with a 3.34 ERA in 31 starts this year.
Also on Friday, the Orioles selected the contract of left-hander Chris Jones from Triple-A Norfolk.