Anzhi have already taken big strides forward as a club, with the likes of Samuel Eto'o, Yuri Zhirkov and Christopher Samba all having moved to Russia, and Guus Hiddink has now taken charge of the club.
Carlos, who acts as an assistant to the president Suleiman Kerimov in addition to his playing duties, has revealed the club are now setting their sights a little higher.
"Today, Messi is the best player in the world," he told Radio Marca. "He continues to show that. Cristiano is the key star for Real Madrid.
"I have no preference for either, but certainly Anzhi will try to sign both when their contracts expire."
Hiddink, meanwhile, has confirmed Anzhi intend to make further additions to the squad this year.
"I think we'll explore some possibilities on the market in the summer, but that is not to say I am unhappy with the players I have," Hiddink said.