Chelsea and Liverpool are reportedly vying for the centre-back's signature, with Van Dijk criticising the club and admitting he submitted a transfer request this week having spent much of pre-season training away from Saints' first-team squad.
A switch to Anfield earlier in the window was curtailed by Southampton accusing Liverpool of tapping up the Netherlands international, leading to the Reds publicly backing out of the deal.
Van Dijk will miss Saturday's fixture at St Mary's Stadium with a virus, but Pellegrino says he will allow the former Celtic man to resume training once he is fit with a view to restoring him to the side.
"My reaction is the same that I said three weeks ago," said Pellegrino. "We are expecting him to come back to train with us because we need the player.
"Hopefully he can change his point of view. The club was clear from the beginning with the player.
"We cannot control every single situation. Virgil is part of our club. He has a contract but we are now waiting."
This week, Southampton completed the signing of Lemina from Juventus for a club-record €18 million, but the coach has not decided if he will play right away.
"Physically, Lemina is good, because he has been training in Juventus, but we will decide between today and tomorrow if he will be part of the team," he said.