Van Dijk was unable to recover after sustaining an ankle injury following a challenge from Jamie Vardy early in the second half of Southampton's 3-0 Premier League victory over Leicester City on Sunday.
The Dutchman was replaced by Jack Stephens in the 55th minute, potentially leaving Puel short of options at centre-back for the trip to Anfield with Jose Fonte having left for West Ham in an £8million deal on Friday.
Puel hopes to have Van Dijk available, but he is not certain whether it will be possible, with Saints protecting a 1-0 lead from the opening leg.
"He could not continue the game. We will see for the next games. I don't know if we can recover him," Puel told a post-match media conference.
"He took a big kick and we will see if we can recover him for this game. We will see in the morning [Monday].
"I hope we can have Virgil of course because he is our captain and he's an important player.
"Of course, it will be better to recover Virgil for this game."
Despite the injury concern and the transfer of Fonte, the Frenchman is not overly concerned about bolstering his options in the centre of defence with a new signing.
"We will see until the end of the market, and we will take things about an opportunity or not to take another centre-back," he reflected.
"I am also happy with the possibilities in defence and we will see if [Florin] Gardos can come back with a good level.
"We will see this with calm and whether there is a possibility or not to take another player in place of Jose."