Anzhi, who face Liverpool at Anfield in the Europa League on Thursday, showed their spending power when they signed Samuel Eto'o last year.
Roberto Carlos, the former Real Madrid player, said the club's billionaire owner Suleyman Kerimov wanted to bring the best players in the world to Anzhi.
Asked if Anzhi would consider an offer for Rooney, Carlos told Sky Sports News: "Why not? He's one of the best players in the world and any team would be happy to have him in their squad. He's still a very young player.
"Of course I could not say when, and if, it will happen. It's not only Anzhi who can want to buy him. There are plenty of teams in Italy and Spain, all over the world, who are eager to have a player like Rooney.
"If the owner of Anzhi has a wish to buy somebody, he will go and do it. But we are trying to change the image of the club. It's not just about money.
"Of course we are going to buy good players but not only international players. We want to sign good Russian players that are not that expensive."