The Dutch defender is being tracked by a host of clubs, including Sunderland, Newcastle United and Hamburg, and has told manager Ronny Deila he wants to go before the close of the window.
Deila and the club are desperate to keep the former Groningen star but the player is adamant he wants out after their Champions League exit.
Van Dijk’s value has also dropped after they lost to NK Maribor and Celtic must decide whether to keep an unhappy player or to take the money.
The Scottish champions are likely to make a substantial profit as they bought Van Dijk for £2.2million and now look like selling him for three times that.
Premier League Talking Points - Gameweek 3
Another top player being sold wouldn’t go down well with the Celtic support, who have seen Fraser Forster, Victor Wanyama, Joe Ledley and Gary Hooper depart over the last two seasons.
The Hoops, however, will make moves to get player of the year Kris Commons on a new extended deal next week.
He is out of contract in the summer and his failure to start either of the Maribor ties has attracted the interest of Norwich, Wigan and Crystal Palace.
Chief executive Peter Lawwell confirmed: “His agent is coming in on Tuesday to discuss an extension because his deal is up at the end of the season. We wanted to get the window out of the way.”
Celtic hope to complete the paperwork on striker Stefan Scepovic’s £2.2m move from Spanish side Sporting Gijon in the next 48 hours.
Celtic could also move other players in and out with misfit striker Amido Balde set to go on loan, with Belgian side Lokeren intested.