Inter will use the transfer fee from Samuel Eto'o's expected move to Anzhi to make a bid for Kaka, according to reports.
A story in the Spanish Marca paper claims that the Brazilian will be targeted by the Nerazzurri before the window closes.
Inter technical director Marco Branca will reportedly touch down in Madrid at some stage this week to hold talks with club and player.
Real would apparently accept an offer of around €30m for the attacking midfielder who doesn't feature in the plans of Real boss Jose Mourinho.
Marca adds that Inter will also consider selling Wesley Sneijder as well this summer to make room for Kaka.
The Brazilian would seem to be a better fit than the Dutchman in Coach Gian Piero Gasperini's 3-4-3 system.
Should the two clubs agree a fee, it does remain to be seen whether Kaka would accept the switch given his Milan links.
The South American spent six years with the Rossoneri before his 2009 move to La Liga.