The Dutch defender has emerged as one of the best centre-backs in Premier League since joining the Saints from Celtic in 2015.
"We'd love to see Virgil van Dijk stay," Black told talkSPORT.
"He's obviously the one everyone has been talking about [leaving].
"It would be wonderful [if he stayed], and would be a big step forward for Southampton if we could keep him.
"But he's one of the best centre-backs in the world, so he may well have options [to leave]."