The Reds make the trip to the Liberty Stadium as they look for a sixth win in a row, taking their unbeaten run to 19 matches in the process.
Van Dijk missed the 4-3 victory over Man City last Sunday with a minor hamstring problem, but he looks set to make his league debut for his new club against the Swans.
“Virgil was back yesterday and completely fine. We have a few problems with players feeling ill or unwell,” Klopp said.
“Raggy was out, but hopefully back today. Dejan was out. Mo Salah was out, but hopefully back today.
“Mo and Raggy are on the good side of it already, but with Dejan we are not 100 percent sure [if he will be back today].”
“It is close, but maybe close and not enough time for Swansea—but [after that] Hendo is back and that’s good news,” he added.
“Alberto is back in training a few days longer and we have to see. Because it is Alberto, he trains all the time and feels it still a little bit—in one or two movements you can see.
“We will not put any rush on him, but he will be back for sure after Swansea as well—or even maybe Swansea, I’m not sure.”
“Clyney is doing well but still a little way to go until he is back in completely normal training. He is doing well, really good.”
The Reds find themselves in a fairly healthy situation with regards to injuries, and with other key men getting back to full fitness, competition for places is set to become ever more fierce.