Darvish (back) threw a bullpen session and took part in fielding practice Tuesday, per MLB.com.
The right-hander has now thrown three bullpens since Friday and appears to be on the verge of a return. Padres manager Jayce Tingler suggested as much Tuesday, saying of Darvish's status, "We're getting close." He could rejoin the rotation as soon as Thursday's series finale with the Dodgers.