The Dutch defender has not featured for Saints since suffering an ankle injury against Leicester in January.
And his long-term future has been the subject of widespread speculation with a queue of clubs keen on getting him on-board.
Van Dijk has been linked most heavily with Liverpool, who have made him one of their top targets this summer.
And that interest has seen him put in a transfer request as he looks to force a move from the south coast to Merseyside.
Pellegrino has confirmed Van Dijk is not available for selection when Swansea visit St. Mary's tomorrow afternoon.
But he says the 26-year-old's absence is down to illness, rather than anything to do with Liverpool's pursuit of his signature.
Asked if Van Dijk will line up against Swansea, Pellegrino said: "No, no, because this week he was with some trouble with a virus. He couldn't train the last two days."
Pellegrino also revealed Southampton retain hope of convincing Van Dijk to stay put.
The Argentine gaffer said: "My reaction is the same that I said three weeks ago. 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 cannt control every single situation. Virgil is part of our club. He has a contract but we are now waiting."
