Hill (knee) is expected to complete a bullpen session of 35-to-40 pitches Tuesday, Bill Plunkett of The Orange County Register reports.
Hill topped out at 20 pitches during his last side session Saturday, so he'll take another step forward by upping that count. If all goes well Tuesday, Hill could advance to throwing live batting practice later this week. Clayton Kershaw (shoulder) is on track to beat Hill back from the injured list, but the latter's eventual return will take on greater importance after the Dodgers lost another member of their rotation Monday. Hyun-Jin Ryu suffered a groin injury in his start against the Cardinals and will move to the IL.