Brazil's Estado de Sao Paulo reported the north American club had identified the Real Madrid  midfielder as the ideal candidate to take over from Beckham as the club's marquee player.
Beckham, 37, is understood to be undecided about whether to continue beyond his current contract, which expires in December.
If the former England captain retires, Galaxy would have the funds to pay up to 27 million euros for Kaka, the report said.
In the event Beckham continues, the club will wait until next year.
Kaka, 30, has been told by Real Madrid coach Jose Mourinho that he is not guaranteed a starting place for the Spanish outfit this season.
The 2007 FIFA World Player of the Year has been strongly linked in recent weeks with a return to former club AC Milan.
Rossoneri officials are still hopeful of securing a deal before the transfer window closes on August 31. (Xinhua-ANI )