The 34-year-old right-hander finished last season with the Padres after being released by the Twins.
But his season ended Aug. 21, when he was hit by a line drive off the bat of the Pirates' Pedro Alvarez and broke his left, non-throwing hand.
The Padres are the eighth team Marquis has pitched for in a 13-year big league career. At the time of his injury, he was pitching his best baseball of the season, with five wins in eight starts following the All-Star break.
He'd allowed three earned runs or fewer in six of those eight starts and had a 3.67 ERA at Petco Park after signing with San Diego.
The Padres came to the winter meetings in hopes of adding starting-pitching depth, and would still like to add one more starter, either via trade or free agency, in addition to signing Marquis.