The Russian billionaire is determined to win the UEFA Champions League, which they very nearly did when Grant was at the helm in 2008, and the Israeli feels that Abramovich will spare no expense for new manager Villas-Boas.
There have been reports that Abramovich is hard to work with but Grant has rubbished those claims.
"It is very easy to work under Roman Abramovich," Grant told talkSPORT. "I have read people in the paper saying that he interferes, but it is not true - he gives you everything you want and you are even sometimes afraid to say something because you know the day after you will have it.
"If you see the [training] facilities at Cobham and even the Academy, it is at a top, top level.
"He is a perfectionist. He wants to achieve the best and he will give you everything to achieve the best, so he wants the results, but he's easy to work with."