"Virgil is still one of our captains," said Pellegrino.
"I'm not thinking about this (changing club captain).
"But being captain for me, it's not a position, it's a decision: if you want to be captain, you have to deserve it."
Asked if Van Dijk deserves to lead the Saints again, Pellegrino responded: "I will think about it.
"Little by little he's getting better. It's difficult to see the best version of Virgil in his first or second game back, but we have to be patient.
"We've got another two weeks after this game due to the international break, and we'll play a friendly game in the middle.
"We're happy with his attitude, he's helping his team-mates."