The Guardians signed Santana to a one-year, $12-million contract Saturday, Jeff Passan of ESPN.com reports.
Santana's agent, Ulises Cabrera, said Monday that his client wants to play for 3-to-4 more seasons, Jon Morosi of MLB Network reports.
Santana went 3-for-4 Sunday with a home run, two RBI and three runs scored against the Reds.
Santana isn't in the Twins' lineup Saturday against Cincinnati.
Santana (illness) is starting at first base and batting in the leadoff spot in Monday's series opener against the Angels.
Santana (illness) is absent from Sunday's lineup against Kansas City.
Santana went 1-for-3 with two walks and a two-run home run in Wednesday's 9-4 loss to the Rays.
Santana is absent from the lineup for Monday's game in Tampa Bay.
Santana is out of the lineup for Sunday's game against the Blue Jays, LaVelle E. Neal III of The Minnesota Star Tribune reports.
Santana went 1-for-3 with a solo home run and a walk in Sunday's 6-5 extra-inning loss to the Rangers.