Chief executive Peter Kenyon and chairman Bruce Buck spelled out the owner's plans in a series of one-on-one meetings - and told Chelsea's players to get on with it.
A Chelsea source said: "The directors got wind of the players' initial reaction to Grant's appointment.
"Some were invited to individual meetings and told Grant is in charge for the long term and has Roman's full support.
"They were also told to expect a lot of stories that he would only be around for a little while and someone else was coming in.
"But it was made very clear that, as far as the owner is concerned, Grant is the future of Chelsea.
"Even if results are bad he will be given the chance to succeed and there will be no knee-jerk reaction."