"We want to make a club of the calibre of Real Madrid or Barcelona," Carlos told Canal Football Club on Canal Plus as he outlined Anzhi's plans to add to a squad that already includes Samuel Eto'o, former Russia wing-back Yuri Zhirkov and ex-PSV Eindhoven winger Balazs Dzsudzsak.
Brazilian World Cup winner Carlos, now 38, was the first big arrival at the club based in the republic of Dagestan, in the Caucasus, in February, and was made joint caretaker boss in the wake of Gadzhi Gadzhiyev's dismissal last month.
With the funds of billionaire owner Suleyman Kerimov being pumped into the club, the former Real Madrid man believes the likes of Anelka, van Persie and Neymar are now realistic targets.
"Anelka is not the only player," Carlos said when asked about possible moves.
"Nene from PSG and Van Persie from Arsenal are players we are following. And Neymar? I talked to him.
"If Real, Barca or Manchester United cannot pay the transfer fee, we will pay it. Suleyman Kerimov can offer what he wants."
Neymar, of Santos, has been heavily linked to a move to Madrid in particular, but no deal has been finalised despite endless speculation, while Anelka's contract at Chelsea is due to expire at the end of this season.
Van Persie, who recently scored his 100th Arsenal goal, has yet to open talks on an extension to his current contract at the Emirates Stadium which expires in June 2013.
Anzhi, whose players live and train in Moscow for security reasons and travel 1,250 miles to Makhachkala for home games, lie eighth in the Russian Premier League.