Oliver, 42, was one of Toronto's strongest relievers last season. He posted a 3-4 record with two saves and a 2.06 earned-run average in 62 games.
Should he decide to return in 2013, he will enter his 20th season in the major leagues. In 716 career games, he has a record of 60-54 with seven saves and 4.53 ERA.
The Blue Jays signed Davis after declining the team option on his previous deal. Davis, 32, hit .257 this past season with eight home runs, 43 RBIs and 46 stolen bases.
Toronto also claimed left-handed pitcher Scott Maine off waivers from the Cleveland Indians. He was 2-3 with a 6.07 ERA in 30 games for the Indians and Chicago Cubs in 2012.
Also Wednesday, the Blue Jays re-instated several pitchers from the 60-day disabled list. They included right-handers Kyle Drabek, Drew Hutchison, Dustin McGowan and Sergio Santos along with left-handers J.A. Happ and Luis Perez.