Ferguson retired at the end of last season, having guided United to Premier League glory, and was replaced by David Moyes, who was subsequently sacked after failing to deliver European football to Old Trafford with Louis van Gaal appointed as his replacement.
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“Ferguson called him [Ancelotti] to be his successor but he told him he had already promised to come here with us,” he said on Spanish radio.
The Italian, who won the Premier League and the FA Cup with Chelsea, has previously denied that he was approached by United.
However, he has revealed that he would be open to managing his country in the future, though he intends to continue with the Champions League winners for now.
"Coaching the your country's national side is always a goal," the 54-year-old told reporters. "But [for the time being] I still want to be on the [training] field every day, I very much enjoy the daily relationship with the team.
"When I am no longer having fun ... I'll call the Italian Football Federation [FIGC]. When [Cesare] Prandelli's contract expires [in 2016]," he jokingly added.