Liriano is set to earn $5.5 million in 2012, while Perkins will make $1.55 million.
The lone Twins player eligible for arbitration who remains unsigned is second baseman Alexi Casilla. Casilla, 27, filed his arbitration figure at $1.75 million, while the Twins offered $1.065 million.
Casilla, who batted .260 with a .322 on-base percentage and .368 slugging percentage in 97 games in 2011, made $865,000 last year.
Perkins, 28, had a career year in 2011, posting a 2.48 ERA with 65 strikeouts, 21 walks and just two homers allowed in 61 2/3 innings. He made $700,000 last season.
Liriano struggled last season, as he carried a 5.09 ERA with 112 strikeouts, 75 walks and 14 homers allowed in 134 1/3 innings. The 28-year-old made $4.3 million in '11.
The Twins haven't gone to an arbitration hearing with a player since 2006, with Kyle Lohse.
They can still reach a deal with Casilla before their hearing, which will be held on an unspecified date between Feb. 1-21.