Flower said: “The prospect of building a new successful England side would excite any coach. I’m motivated.”
Asked if Cook is the right man to lead England, Flower added: “Yes, he is.”
Flower will hold meetings with Paul Downton, who recently replaced Hugh Morris as the England and Wales Cricket Board’s new managing director, after the Test in Sydney which starts on 3 January to discuss his future.
The 45-year-old has held the position since replacing Peter Moores in April 2009.
And former Zimbabwe wicketkeeper Flower says the potential challenge of rebuilding the England team is one which excites him.
“This is a challenging time for any leader,” Flower continued. “Out of challenging times we can grow significantly and we’ll be looking at how we will do that.
“I’ll be meeting with Paul Downton in Sydney and we’ll be talking about the future leadership of the England team.
“I’m proud to have been a part of it so far. Any coach would be excited to work with the likes of Joe Root and Ben Stokes.”
Cook has already voiced a desire to remain as captain despite England’s poor performances and Flower believes he should carry on.
“Alastair Cook has captained six Test series and this is the first serious loss,” Flower added. “He’s done some outstanding things with the bat but also as a leader.”
However, former England batsman Geoff Boycott has severe doubts about Cook’s ability to captain England, and suggests in the Daily Telegraph he lacks the tactical knowledge and strong personality required to lead the side.
He said: “Somebody at the England and Wales Cricket Board has to decide if Cook is the right man to captain the team. I don’t think he is.
“I don’t judge captains on whether they win every series. I judge my leader on whether he has fantastic tactical knowledge about the game. You cannot teach it. You are born with it.
“You have to have a feel for the nuances of cricket as the game changes and stay one step ahead of what is happening. There is no rule book. If you do not have the tactical gift then you need a wonderful personality that lifts people and gets them behind you in tight situations.
“I don’t see Alastair having either of those traits.”