The 22-year-old only joined Celtic last summer but a series of impressive displays for the Scottish champions has seen the Dutch defender linked with a move away from the club.
Gary Monk is looking to offload Chico Flores this summer as well as Michu and their transfers will fund a £6 million move for the promising young defender.
However, Celtic are keen to keep hold of their star who signed a four-year contract last June in a £2.6 million switch from FC Groningen, and have said that only a "crazy" offer will tempt them to sell.
He made 47 appearances in all competitions last season and scored five times to help The Hoops lift the Scottish Premier League for the third successive year.
Sevilla are also keen on a move, with new Southampton boss Ronald Koeman eyeing up a move as he looks to rebuild The Saints squad ahead of the new campaign.
Although Celtic remain keen to hold on to their star defender, a big offer could be too much to refuse, and van Dijk could well be playing in the Premier League next season.