Ancelotti was in charge of Juventus back in 2000 when they appeared certain to win the Serie A title after holding a five-point lead with three matches remaining - having led by nine points five games earlier.
But a major collapse saw them famously pipped to the title by Sven-Goran Eriksson's Lazio on a dramatic last day of the campaign.
Still in the hunt: Carlo Ancelotti is refusing to rule out a Man United collapse
A Chelsea comeback in the current Premier League title race would be even more sensational, with Ancelotti's men having trailed United by 15 points at one stage, which was in danger of being 18 when they were 1-0 down to United at Stamford Bridge last month.
But a 2-1 victory sparked a run that has now seen them take 22 of the last 24 points on offer.
Although United had a brief blip after losing to the champions, there has been no sign of them suffering the kind of slump Juve endured under Ancelotti, with their lead currently a comfortable six points.
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But their next two games are at Arsenal and against Chelsea and Ancelotti has insisted anything could happen in the next fortnight.
He said: 'I lost a title nine points up with eight games to go. It can happen.
'It's not a nice feeling.
Painful memories: Sven Goran Eriksson celebrates winning Serie A with Lazio in 2000 as Ancelotti looks on
'It was very difficult to think two months ago that we could stay with the lead so for this reason, at this moment, we are happy.'
Chelsea's only realistic hope of snatching the title would be to win all of their remaining games - including at Old Trafford in two weeks - and hope Arsenal beat United on Sunday.
A Blues victory over Tottenham on Saturday would crank up the pressure on United ahead of that game, according to Ancelotti.
Crucial game: Chelsea face Tottenham on Saturday
'If we are able to win against Tottenham, I think we can put more pressure on Manchester United in the game against Arsenal,' he said.
Were Chelsea also to win at Old Trafford, the teams would be level on points with two games remaining, raising the prospect of the title being decided on goal difference.
'It can happen,' said Ancelotti, whose side's 3-0 victory over West Ham on Saturday saw them close to within two goals of the leaders.
'It was important for us to score three goals.'
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