The Dutchman has not featured for the club since early 2017 but is back to full fitness and has recently returned to training.
Van Dijk had went on strike at the South Coast outfit after attempting to push through a move to Jurgen Klopp's Liverpool.
However, with Southampton refusing to sell him, van Dijk is now trying to get back into the first-team fold.
But new manager Mauricio Pellegrino has said the former captain will not be receiving the armband upon his return to action.
Speaking in the pre-match press conference, the Saints boss stated that he will make a late decision on whether to bring the defender back into the squad for the trip to Selhurst Park.
"Virgil was training well. He played 90 minutes the other day in the reserve game, but tomorrow we will decide [if he’ll be involved against Palace].
"Hopefully he will be getting better every single week but I am happy with that because it’s not just about Virgil, it’s everybody right now ready to be part of the team.”
Pellegrino, however, did admit he had reservations about giving returning the captaincy to van Dijk.
"For me the captain is someone who the team may decide and something that you have to deserve – not something the manager can give the player to be a captain," said the former Alaves boss.
"You cannot be captain if you’re not playing. Obviously Virgil was one of the leaders of the squad.”
Southampton face Roy Hodgson's Crystal Palace this weekend.
