Indeed, the 24-year-old defender has been linked with Southampton recently by Sky Sports among many others, while several suitors have been suggested all summer long.
And the natural response from Celtic fans has been that of hoping the club will fend off Southampton or any other Premier League interest. Especially as Champions League football could well be enough to keep the Dutchman at Parkhead this season.
But Walker has suggested the Bhoys' keen nose for turning a profit on a player may well persuade them to negotiate over Van Dijk, overriding their natural instinct to issue a hands-off warning.
Walker told Sky Sports News: "Celtic will be aware of the fact there is business to be done and remember this is a player who only cost £2.5m when he signed two years ago.
"Celtic have done good business in the past by selling on players that they have bought cheaply - the likes of Gary Hooper and Victor Wanyama spring to mind - and I think that by the end of the transfer window Van Dijk will be playing his football in England somewhere."
Southampton are in need of a centre-back, as are a number of their rivals, with Van Dijk's ability on the ball making him a very appealing choice to many like the Saints.
Should Celtic qualify for the Champions League, however, it could genuinely be a 50-50 as to whether the 24-year-old leaves Scotland this summer.