The midfielder has been ruled out for at least a month after surgery on a groin problem, which will mean he misses a minimum of five matches plus England's World Cup qualifiers against San Marino, Albania and Poland in late March.
"The best-case scenario, I don't know to be honest," he said of Henderson.
"It's not a quick one but of course we all hope there is still a possibility for him to play a few games this season, but we will see."
Henderson will not return to the club's AXA training complex for a while but when he does Klopp expects him to continue to be an influence in the way his other injured senior players have been.
"They all have to be influential. So many injured players not available at the moment and most of them are leaders in this group," he added.
"Hendo is not here yet but Virgil, Milly (James Milner), Joel all have to be influential and that is what they will be and when Hendo is back he has to play this role while doing his rehab."
Klopp, who due to coronavirus restrictions was not able to attend the funeral of his mother Elisabeth in Germany after she died in January, will give Alisson all the time he needs following the tragic news of his father on Wednesday.
"No comment about that. There's nothing to say. I don't want to read anything tomorrow I said this or I said that. It's not the time for that," said the Reds boss.
"We didn't think about that (him playing on Sunday) so far, really."
There has been some good news on the injury front with forward Diogo Jota returning to full training this week after three months out with a knee injury to put himself in with a chance of making the squad for Bramall Lane.
Fabinho, who has played just one of the last seven matches because of a muscle problem, and Milner, who has missed two games with a hamstring injury, are also set to begin training on Saturday but they may not be risked for Sunday.
Jota's availability, however, could be the lift Klopp's side need after just two Premier League wins since Christmas dropped them to sixth in the table.
"Diogo trained now twice with the team, looks very good – very good. He was out long term so we have to see what we can do with that but in training he looks really promising," said the Reds boss.
"Yes of course, the way he came back in training is very positive. We just have to make a decision about what makes sense for him, when does it make sense (to play him)."