Versteeg suffered a metacarpal fracture in his left hand when he was struck by a puck during the Winter Classic on Jan. 1. He underwent surgery on Jan. 6 to stabilize the fracture and was expected to miss four weeks.
Versteeg still has a cast on his hand and has not resumed skating.
"Maybe it was going to be a little bit longer than that, but we said around four [weeks]," Quenneville said prior to Wednesday's game against the Pittsburgh Penguins. "We'll see. It'll probably be a little bit longer than that."
Quenneville said there's a possibility Versteeg could join the team during their upcoming six-game road trip. They play on the road from Jan. 28-Feb. 8 following the NHL All-Star Game.
Versteeg has nine goals, 18 assists and is a plus-14 in 34 games this season. He will miss his ninth consecutive game due to the injury on Wednesday.