The 23-year-old Dutch centre-half is the subject of interest from a number of clubs, including Spanish club Sevilla, following an impressive last season at the Scottish champions.
Sevilla see Van Dijk as a possible replacement for their captain Federico Fazio, who has signed for Tottenham Hotspur, and both Ronald Koeman and Gus Poyet are keen to strengthen their defensive units before the deadline on September 1.
Sky sources understand Celtic remain reluctant to sell Van Dijk and have not yet received any bids for the player, but they crashed out of the Champions League qualifiers on Tuesday night with a home defeat by Maribor and the player wishes to leave the club.
Celtic were criticised by Sky Sports’ Scottish football experts Charlie Nicholas and Andy Walker for not backing new manager Ronny Deila in the current transfer window and becoming “a selling club”.
Former Celtic striker Walker said: “It’s really depressing that Celtic didn’t make a really strong case for their manager.
“They didn’t back him with the signing of players. They consistently lose their best players and it’s a huge disappointment for the supporters. Celtic right now are very much a selling club.
“If they get a semi-decent offer for Van Dijk I think they’re more than prepared to sell him.”
Van Dijk joined Celtic from Groningen in 2013, signing a four-year-deal, and has made 51 appearances in all competitions, scoring seven goals.