Flower, one of the principal architects of England's brief rise to the pinnacle of Test cricket in 2011, is contracted to the end of the Ashes which wraps up with the fifth and final match in Sydney.
Both Flower and Cook have faced calls to step down from their positions after England's eight-wicket loss at the Melbourne Cricket Ground on Sunday, which gave the hosts a 4-0 lead in the series.
"Paul Downton the new managing director has arrived in Australia and I'll be meeting with him in Sydney," Flower told reporters in Melbourne on Monday.
"We'll talk about the leadership of the national team with regards to the coaching position.
"I'm very motivated to contribute to English cricket and that's what I'm going to do."
Former England wicketkeeper Downton was appointed in October to take over from the outgoing Hugh Morris in February but is making a special trip Down Under to cast his eye over the team.
The entire England staff is set to be reviewed after the fifth Test in Sydney and Flower's possible departure would likely be followed by several more, including batting coach Graham Gooch.
Cook's captaincy has come under mounting scrutiny with each loss in the Ashes tour, and by any measure, the 29-year-old endured a poor Test in Melbourne.
Apart from dropping two catches at first slip in the first half-hour of day four when his team needed quick wickets, Cook's field placements and bowling changes were heavily criticised by former players and pundits on both sides.
"He doesn't have a natural feel for the game," former England batsman Mark Butcher told ESPN.
"He isn't able to spot things before they happen or he isn't able to react quickly to things as they happen ... Tactically he was absolutely awful."
Since taking over the captaincy from Andrew Strauss in 2012, Cook has led England to a breakthrough series win in India and their third successive Ashes win earlier this year on home soil.
However, a collective loss of form from his senior players in this Ashes tour has exposed Cook, who has not scored a century in his past nine Tests and has appeared powerless to influence the course of matches Down Under.
"Alastair Cook has captained six Test series for England and this is the first loss he's had," Flower said.
"He's done some outstanding things for England with the bat and he's also done some excellent things as a leader in the dressing room and out on the field.
"We are all responsible for this result - management and players."
Flower said he expected there would be "one or two" changes for England for the Sydney Test, Australia's only spin-friendly wicket.
With the series shot, England may be tempted to give rising legspinner Scott Borthwick a chance and bring in a fresh paceman in either Steve Finn or uncapped Northern Irishman Boyd Rankin.
Pundits have also demanded Ian Bell be moved up to number three in place of Joe Root, who has struggled in the position vacated by Jonathan Trott when he left the tour after the first Test in Brisbane.
Jonny Bairstow, who disappointed with his glovework in Melbourne after replacing the dropped Matt Prior, may also be shunted out to reinstate Prior.
"We don't want people to accept losing too easily but sometimes you have to face the fact that you've been outplayed," Flower said.
"The Australian side has done exactly that to us. But I don't believe we should be totally distraught at where we are.
"A lot of these cricketers have had outstanding success on the international stage and they will have success again."