"Obviously when you lose Geno, it's a tough loss from our standpoint for everything that he brings to our team. But we are certainly encouraged that, hopefully, we will get him back in a timely fashion," Sullivan told reporters Friday.
Per Dave Molinari of DK Pittsburgh Sports, the Penguins coach added there's "a strong possibility" the 34-year-old will return during the regular season.
Malkin was hurt during the first period of Tuesday's game when he was levelled by Bruins defenceman Jarred Tinordi.
Prior to the injury, Malkin had been red-hot on an eight-game point streak and had 24 points in 29 games this season after a slow start.