Benitez took over from Roberto Di Matteo following the Blues' exit from the Champions League, and has since endured a testing time from the club's supporters.
Abramovich, though, expressed his satisfaction with Benitez's tenure thus far, and said as much to the manager after Chelsea defeated rivals Arsenal on Sunday.
"We have people that talk with him and I have the information," Benitez said. "The other day I had time with him and he was really pleased. He was really pleased with the game.
"He has ideas. I have ideas. We share ideas. We explained to each other what we're trying to do. It's fine."
Chelsea were in contention for seven trophies at the start of the season and now it is three, including the Capital One Cup, where Benitez's side must overturn a 2-0 deficit at Swansea in the semi-final second leg on Wednesday.
"In a transitional period - we have new players and some of them are at the end of their contracts - I think it's a team that is growing and is improving," Benitez explained ahead of the game.
"As a manager you have to be satisfied with this. As a manager of a top side you want to win trophies; still we have to try to do better to win trophies.
"I think the priority for the club is to be in the top four and try to win trophies at the same time. If you talk with the players they say we're going in the right direction."