The Blues confirmed Abramovich spoke to Villas-Boas during a rare visit to the club's training ground on Saturday before attending Sunday's Premier League game at Stamford Bridge.
But they insist the Russian billionaire - who has sacked almost every manager who has failed to win the title during his nine years as owner - remains fully behind the 34-year-old's project, after a report he had become frustrated with results under the Portuguese.
The fourth-placed Blues now lie a massive 14 points behind leaders Manchester City and just a point ahead of fifth-placed Newcastle.
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 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."