The big-spending Dagestan outfit hit the headlines in the summer when they made Samuel Eto'o the highest paid player in world football with a deal worth in excess of £250,000-a-week.
Billionaire Suleyman Kerimov is financing the club and despite already making huge investment, they are still looking for more big names.
Having already been linked with England coach Fabio Capello, along with midfielders Frank Lampard and Steven Gerrard - Roberto Carlos admits they have other targets in the Premier League.
"Anelka is not the only player. Nene from PSG and Van Persie from Arsenal are players we are following," the Brazilian told TV show Canal Football Club.
He also confirmed that the club are still tracking Brazilian wonderkid Neymar.
"Neymar? I talked to him. If Real, Barca or Man United cannot pay the transfer fee, we will pay it. Suleyman Kerimov can offer what he wants."
Meanwhile, Anzhi's Hungarian winger Balazs Dzsudzsak has backed the club's stance for looking at big names.
Dzsudzsak says it is great to know that his club has the chance to sign players like Samuel Eto'o or Gerrard or a coach like Capello.
"It doesn't matter what I feel, but it's important that we know it's a reality that players like them can sign to us," he told Origo.
"When I signed for Anzhi, I received so many critics [from Hungary] and now this thing [that some players are going to leave their team for Anzhi] is a positive feedback for me. It makes me calm and I feel good when I think about it.
"Before the summer transfer period, nobody knew a word about Anzhi and now the club signed a player from Inter and having talks with Fabio Capello, Guus Hiddink and other star coaches.
"I'm sure it may be frustrating that there's a region which was not on the football map and suddenly Europe is talking about who they could or who they might sign."