24-year-old Dutch centre-back van Dijk has impressed over the course of his two seasons at Parkhead and could well be an ideal summer capture.
Celtic brought in Virgil van Dijk from Groningen in June 2013 and he has already made 106 appearances for the Glasgow club, playing a crucial role in back-to-back domestic title triumphs.
The Daily Mail believe Martinez is on the look-out for defensive reinforcements as the Spanish boss has seen Sylvain Distin join Bournemouth, while Stones continues to be linked with a move to Chelsea.
Chelsea failed with an opening £20m bid for England international Stones [via Independent] but are ready to put in a fresh offer of £26 million for the 21-year-old Goodison Park starlet [via The Guardian].
Everton saw their Europa League involvement lead to a detrimental effect on their Premier League standing in 2014/15, with the Merseyside outfit finishing outside the top-half of the table for the first time since 2006.
Martinez has seen a number of his top players linked with moves away this summer with Kevin Mirallas an apparent West Ham United target [via Goal] whilst striker Romelu Lukaku said to be on the Manchester United radar [via Independent].