Luka Modric, who turns 40 in September, joined Madrid from Tottenham in 2012 and has been linked with a move to Italy since early June, after announcing he would leave the Spanish giants at the end of his contract.

Madrid play Paris Saint-Germain in the semi-finals of the Club World Cup on Wednesday. The final is on July 13.

"He'll arrive in August," Allegri said during his first press conference on his return as Milan boss.

"He's an extraordinary and important player, it would be useless to talk more about him."

Allegri is back at the helm at Milan having led them to the Serie A title in 2011 during his first spell in charge between 2010 and 2014.

Their first game of the new season is in the Italian Cup on August 17.