Grant's future has been the subject of speculation ever since he replaced Jose Mourinho as manager early in the season.
Buck did admit that he was pleased with Chelsea's position in the Premier League and their progress to the semi-finals of the UEFA Champions League, and Grant is also happy with the season as a whole.
He concedes that turning Chelsea into a more entertaining team is very much a work in progress, and has told billionaire owner Roman Abramovich to fire him if he feels he is not doing a good job.
"I have told all my owners that if the club at any stage are not happy they can tell me and I will go," said Grant.
"It is not a matter of money and I am sure that if I was not happy at some stage and wanted to go, the club would understand. All my life it has been like this and it won't change.
"I agree with Bruce about the situation of the team. Nobody thought we would be in this situation when I took over the team.
"I came to lead another way, a different way, we have seen that it will take more time. But we have won a lot of games and the football is good.
"Of course, it is not 100 per cent but it is good. I need to do my job. We are together."