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.
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.
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.
"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.
"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 Sunday saw them close to within two goals of the leaders.
"It was important for us to score three goals."
It was even more vital one of them was netted by Fernando Torres, who finally began to repay his £50million transfer fee.
The Spain frontman's strike - his first in 901 minutes for club and country and 732 in a Chelsea shirt - sparked wild celebrations from both players and fans.
Ancelotti said: "I've never seen this kind of reaction for what was an important goal.
"He is a humble man, a humble player - this is the reason the people love him."
Ancelotti revealed after Sunday's game he would spend the build-up to the Spurs match trying to get Torres and Didier Drogba into the same side.
The pair have failed to strike up an understanding since the former's move from Liverpool but their manager was adamant they could.
Ancelotti, who should discover on Tuesday the extent of the "muscle" injury that saw Michael Essien limp off on Sunday, added: "I think we can start them, but now I cannot say if they start against Tottenham."
Hammers boss Avram Grant was also unable to say whether Football Writers' Association Player of the Year Scott Parker would be fit for his side's trip to Manchester City on Sunday.
Talismanic midfielder Parker has sat out the last two games with an Achilles injury and has been badly missed as West Ham have slipped back to the foot of the table.
Grant said: "I want him to play. It depends on his condition.
"He's not feeling so good and I hope that he will be available for us soon.
"The good news is maximum two weeks he will be fit, maybe next week also."
If not, West Ham need to learn to play without Parker - fast.
Grant, who predicted his side needed between seven and nine points to survive, said: "Every player wants to play with a good player - he's the player of the year.
"But he didn't play and we need to play also without him."