Milan confirm Taiwo and Mexes captures
"In defence, Milan are sorted. We have taken Mexes and Taiwo," Allegri told a news conference on the eve of their Italian Cup semi-final second leg at Palermo.
Nigerian left-back Taiwo, who the Rossoneri are trying to sign as an EU player if he can gain a relevant passport, will fill the only troublesome spot in Milan's line-up this term.
The 26-year-old has been with the French champions since 2005.
France centre-back Mexes, out with a cruciate ligament injury, said last month that he would probably be joining Milan in the close season after seven years in the Italian capital.
Milan's ageing squad is in need of renewal despite their scudetto triumph and a possible first league and cup double.
Several players including out of favour midfielder Andrea Pirlo are out of contract in the close season and others are in their mid-30s.
"When the season is over we will talk with the club," Allegri said of Pirlo's situation while responding to questions about media speculation linking Milan with former playmaker Kaka - now at Real Madrid - and Santos's Brazilian youngster Ganso.
"The first has won everything in his career and the second must still learn a lot," Allegri said.
Owner Silvio Berlusconi loosened the purse strings this term to bring in the likes of Zlatan Ibrahimovic having previously reined in spending during the global economic crisis and watched Inter win five straight scudettos.
However, the two free transfer deals show the Italian prime minister is still keen on a bargain when he sees one.