In the three games under the Spaniard so far the Blues have taken just two points, twice drawing 0-0 before then losing 3-1 to West Ham at Upton Park.
The slump in form has seen them fall 10 points behind leaders Manchester United in the Premier League with rumours suggesting that the Russian was interested in bringing back former manager Avram Grant in an advisory role, claims which Benitez denied.
"All the information I have is he is not coming," he declared to reporters, "so for me it is just a story in the press."
The 52-year-old is adamant that he has a good relationship with Abramovich and has his full support.
"I spent a lot of time with him the last 10 days," Benitez continued. "After [the defeat to West Ham], people were talking to him. We spoke and said the first half was so good. We then made a mistake and we have to find solutions.
"The team looks stronger in defence but we have to analyse the problem we have.
"We have to manage better against teams that are strong physically. There are positives but there are things that we can improve."