Ancelotti has been in charge at the San Siro since 2001
AC Milan have rejected an approach from Chelsea for permission to talk to coach Carlo Ancelotti about the vacant manager's position at Stamford Bridge.
The Premier League and Champions League runners-up began their search for a new boss after sacking Avram Grant.
"(Chelsea) asked for our permission and naturally everything stopped there," Milan vice-president Adriano Galliani told the Serie A club's website.
"He and another Italian coach were at the top of Chelsea's list."
Chelsea sacked Grant on 24 May - three days after losing to Manchester United in the Champions League final - and also terminated the contract of assistant first-team coach Henk ten Cate five days later.
BBC Sport understands the other Italian coach to be Roberto Mancini, who was dismissed by Inter Milan this week despite leading the club to three successive Serie A titles.
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