After England's 150-run defeat in the third Test in Perth, which gave Australia a 3-0 lead with only two Tests to play, Flower was asked about his future but would only comment on the upcoming matches in Melbourne and Sydney.
"We have two Tests and I am hungry to do well in those games," said the 45-year-old. "That is as far as I am looking at the moment."
As well as the three Ashes triumphs, Flower also led England to the top of the world Test rankings in 2011 and the World Twenty20 title in 2010.
But, after three heavy defeats in Australia brought the Ashes defence to the quickest possible end, Boycott believes Flower and his staff must take some responsibility for England's shortcomings.
"Some of our coaching staff should have a serious look at themselves because we are on the down and Australia are on the up," added Boycott, who scored 8,114 runs in Test cricket.
"Australia have had more energy, looked up for the challenge. They have plotted and planned better."
But England captain Alastair Cook defended his former Essex team-mate, insisting he wants Flower to continue.
"He's an outstanding coach, let's make no mistake about that," said Cook.
Batting let England down - Vaughan
"He's an outstanding person, and a great person to have around - especially for me as a captain, the advice he gives me.
"It's not down to him that we've lost, it's that we haven't had enough players in form."
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