Malkin has missed the past seven games because of an undisclosed injury. The forward skated on a line at practice with Scott Wilson and Patric Hornqvist, and also was on the top power-play unit with Hornqvist, Sidney Crosby, Phil Kessel, and Kris Letang.
Malkin's 44 points (22 goals, 32 assists) are tied with Dallas Stars forward Tyler Seguin for seventh in the NHL.
Forwards Carl Hagelin (concussion) and Conor Sheary (upper body) also skated Monday. Hagelin, who hasn't played since Feb. 4, remains in concussion protocol.
"He's still status quo," Sullivan said. "We'll see how he responds after today and we'll go from there."
Although Sullivan is encouraged with Sheary's progress, forward Bryan Rust (upper body) likely will remain sidelined for the long term. Rust left in the second period of a 4-1 win at the Colorado Avalanche last Thursday.
"He's still being evaluated," Sullivan said, "so reluctant to put a time frame on it at this point."
