Speculation in recent weeks has suggested the 45-year-old, who first took the role of England coach in 2009 and has guided them to three Ashes successes, will step down from his role following the ongoing series in Australia.
However, Collier expects the former Zimbabwe batsman to remain in in the role after the current tour, where England have relinquished their hold on the Ashes after trailing 3-0 with two Tests remaining.
"It has obviously been disappointing to lose the Ashes after such a successful run," Collier told Sportsweek.
"Expectations were high and clearly we have under performed.
"We have to give credit to Australia, they have fully deserved Ashes victory - we have got no excuses.
"Andy has the total, full confidence of the board. He has done an outstanding job, not just as England team director but prior to that.
"We believe we have got one of the best men in world cricket and we hope Andy will take us forward well in to the future and certainly in to the 2015 Ashes.
"He certainly has our full backing. We believe he is the best man for the role and we see no reason to change that. We believe Andy is one of the best coaches, not only in world cricket today, but one of the best coaches of all time."
Collier will be in Melbourne for the fourth Test but does not anticipate holding conversations regarding Flower's future whilst the current series is ongoing.
He said: "We have had discussions with Andy, he is always very committed to England and clearly everyone assesses their position from time to time but all I can say is that the ECB feel we have an outstanding coach.
"We will wait until well after the series, I don't think it is appropriate to talk in those matters during a series, Andy wouldn't want that and we don't want that.
"We have two Test matches to win but we are very confident he will lead us to further success in the near and medium-term future."