Quentin, 33, played in just five games with Seattle's Triple-A Tacoma team in 2015.
The Mariners signed him after he was released by the Atlanta Braves.
Quentin offers the Twins depth on the outfield corners and would make $750,000 if he earns a spot on the team, according to reports.
Multiple knee injuries have plagued the former first-round draft pick out of Stanford. In 2008 with the Chicago White Sox, Quentin hit 36 home runs and drove in 100 runs.
Quentin last played in the majors, playing in 50 games and batting .177 with four home runs in 2014 for San Diego.