The Daily Mail reports that Kaka has been offered to United on a season-long loan.
Real Madrid are keen to let Kaka leave as they expect to sign Luka Modric before the transfer window closes.
Galatasaray and AC Milan have also been linked with the 30-year-old.
Kaka did not feature for Real Madrid in their opening game against Valencia on Sunday night.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.