Voss said Black was "unlikely" to play St Kilda at the Gabba on Saturday night, and would possibly be considered to play Richmond the following week.
The 2002 Brownlow medallist has missed four matches since last playing Hawthorn in round 14.
He was initially expected to miss just a week or two.
Aside from some light running and kicking, Black has done little training since.
"It is (dragging on)," Voss said on Tuesday.
"He hasn't trained for a month so it's hard to think he'll get up."
Another midfielder under an injury cloud is Brent Moloney who came off late in Sunday's loss to Port Adelaide with hamstring soreness.
The Lions are not overly concerned, though, and expect him to play the Saints.
Voss said despite being out of the finals picture, the Lions had plenty to play for in the final five weeks.
"We are playing young players, we're backing them in, they're improving as a group. I'm happy with how the plan's unfolding," he said.
"We're in a mode where we're turning up every week to compete to win. If we fixate on anything else other than that, sport has a great way of being able to slap you around the face. We're not after that slap.
"We have to capitalise on some of the work we've put in in the last month and finish off the season strong."
Michael Whiting is a reporter for AFL Media. You can follow him on Twitter: @AFL_mikewhiting
