The Blues confirmed Abramovich spoke to Villas-Boas during a rare visit to the club's training ground on Saturday before attending Sunday's Barclays Premier League game at Stamford Bridge.
But they insist the Russian billionaire remains fully behind the 34-year-old's project, following a report he had become frustrated with results under the Portuguese.
A spokesman said: "Roman likes to get down to Cobham and watch training whenever he can. He was able to visit on Saturday and he and Andre had a good chat after the training session, which is normal."
It is thought Saturday was the first time Abramovich had watched Chelsea train this season, with the 45-year-old's focus having been on his high-profile court case with former associate Boris Berezovsky.
He spent 35 minutes casting his eye over the session before spending another 20 speaking with Villas-Boas.
He also spent half an hour talking to players in the dressing room after Sunday's game, which saw Chelsea controversially held to a draw having led 3-0.
The match provided just the kind of entertainment Abramovich is believed to demand, but represented more points lost from a winning position by the Blues at home this season.
Juan Mata, who scored a stunning volley and also set up the third goal, told Chelsea TV: "After that, the game was crazy. It was so fast, without midfielders, and it was box to box."
The winger, who joined from Valencia last summer, added: "Here, it's faster than Spain. Until the 90th minute, you haven't got the three points. Man United is a very, very good team and they always try to win and to draw."
United needed two penalties to get back into the game, the second particularly controversial.
Villas-Boas was critical of referee Howard Webb but managed to steer clear of comments that might have landed him a Football Association charge.
Opposite number Sir Alex Ferguson was also angry with the officials, claiming Gary Cahill should have been sent off for what he considered a last-man challenge.
Cahill, who made his Chelsea debut, said: "At the time I thought I had got the bottom of my studs on the ball.
"I have seen the replay and sometimes when you go through the player and across the player to get the ball they are given against you, so I was fortunate to get away with that one, but if you see the direction the ball moves I think my studs actually touched it first."
He added: "It was a fantastic game to be involved in and it was in at the deep end, but these are the games you want to be involved in.
"However, any game you go 3-0 up in, you expect to win, so that has put a dampener on my debut. It is a sickening feeling like we have lost the game. The mood is a bit flat and we are disappointed."
Chelsea now lie 14 points behind leaders Manchester City and, perhaps more importantly, just one ahead of fifth-placed Newcastle.
Villas-Boas has repeatedly declared he has no doubt he will still be in charge at Stamford Bridge next season, despite Abramovich having sacked almost every manager who has failed to win the title during his nine years as owner.
The Russian appears to be more patient with the current regime, perhaps recognising the squad needs a significant overhaul before being able to challenge United and City.
However, failure to qualify for the Champions League may test that patience to the limit.