United currently sits second in the table behind their neighbours Manchester City and between the pair, they have scored 32 goals between themselves through just five games.
Southampton, meanwhile, secured a clean sheet in the win against lowly Crystal Palace, but United presents the opposite problem with Romelu Lukaku running rampant meaning van Dijk could be drafted in to start at St Mary’s.
“We’ll decide tomorrow, but every single week Virgil is important because he is getting better,” said Pellegrino ahead of Saturday’s game. “After a long period of time without playing a game he is training well. It’s good news for us, because we need Virgil, like every single player in our squad.”
Van Dijk is coming off another runout with the Under-23s where he scored Saints’ opening goal with a calmly placed header, after making a cameo appearance in the closing minutes at Palace.
“Virgil is a very important player for us,” said Pellegrino. “I think every single week he will improve, but at the same time he needs to train and play, because for me the best training session is playing games.”