Ings has been sidelined since October and his knee injury was expected to sideline him until the end of the campaign.
But the one-time England international could yet be back before 2015-2016 is over, with manager Jurgen Klopp revealing the 23-year-old is nearing a return to training.
"Danny's in a really good way after a serious injury but he's not back in team training yet," Klopp said.
"Maybe two weeks, I'm not too sure, it was four or five days ago when someone sent me the email saying it was two weeks until he could train with the team.
"I don't know yet if he will be able to play again this season. That all depends on how he recovers and how he's training. He's been out for a long time."
Klopp also had positive news on midfielder Can, who ruptured ankle ligaments in his side's remarkable Europa League win over Borussia Dortmund on 15 April.
However, Klopp is remaining cautious over just when he may have the 22-year-old available again.
"He's recovering much better," he said.
"There might be a new timescale but I'm not telling you because there is no proof yet, but he is very good."
