The Mirror reports that Guus Hiddink’s side are prepared to offer the 28-year-old a three-year contract worth £300,000-a-week deal.
Hiddink has been given a blank cheque to go and sign three world class stars this summer.
Hiddink said: “In this summer’s transfer period we are going to get a couple of really well targeted investments to build this Anzhi team into an even bigger side in world football.
“We have made it possible to break into the top five in Russian football. We are now among the traditional strong teams from Moscow and St Petersburg. But we need to make even bigger steps than we have done so far, to play for the top spots.
“Initially I was not going to put my eye on a Dutch player, but now I am not ruling out that this could take place.”
Anzhi will face competition from the likes of Manchester United and Manchester City in the race to sign Van Persie.