The team is looking to build pitching depth in case incumbent starters Marcus Stroman or Aaron Sanchez get traded. There has been growing interest in the two hurlers and general manager Ross Atkins hasn't ruled out the possibility of a move.
Both Fiers and Graveman finished the 2018 campaign as members of the Oakland Athletics.
Fiers, 33, was acquired from the Detroit Tigers in early August and was generally reliable the whole season. He went 12-8 with a 3.56 ERA and 1.18 WHIP over 31 games.
Graveman underwent Tommy John surgery in July and is expected to miss at least a portion of the 2019 campaign. He went 1-5 with a 7.60 ERA and 1.66 WHIP over seven starts this past season.
The 27-year-old was an eighth-round draft pick of the Blue Jays in 2013. He was later part of the package sent to the Athletics in exchange for third baseman Josh Donaldson in 2014.