The club's vice-president is in Madrid to negotiate with the playmaker but has stressed that time is of the essence as the Serie A club look to bring the Brazilian back to San Siro
The Brazilian moved to the Bernabeu from the Rossoneri in 2009 but struggled to make an impression during his four years in Spain.
He confirmed that he wants to leave the club earlier this week, with Galliani now in Madrid to thrash out a deal with the player.
"The arrival is difficult," he told reporters.
"I'm here. It's tough, we'll see. He has to say yes tonight because he'd need to be back in Milan tomorrow for a medical."
Kaka represented Milan for six years, winning the 2007 Champions League with the club and claiming the Ballon d'Or that year.