Flower's team completed their 3-0 series victory over Australia after a dramatic drawn fifth Test at The Oval on Sunday, but the Zimbabwean had little time to celebrate before being quizzed about his future.
Less than 24 hours later, Flower responded to reports at the weekend that he may quit his current role after the return Ashes series in Australia later this year.
Reports suggested Ashley Giles, England's one-day international and Twenty20 coach, was being lined up as his replacement.
Flower handed over the reins of the limited-overs teams to Giles at the start of the year, a move designed to give him more time at home and less on the exhausting international treadmill.
The 45-year-old, who was appointed as England's team director in 2009 after a spell on the backroom staff, stopped short of pledging himself to the role long-term, but also gave no obvious hint that an exit is imminent.
Asked if there was anything to reveal about his position, Flower said: "No, there is not. I don't like to look too far ahead with regards to my own personal situation.
"We have an away Ashes coming up and I'm reflecting on a job well done in this series by the players, who should feel very satisfied and very proud.
"There's always another exciting challenge around the corner and in this instance it is the Ashes away."
Amid all the talk of Flower's future, it was almost possible to overlook the contentious end to the Ashes at The Oval.
England needed just 21 runs in 24 balls when the umpires ordered the teams off for bad light, following established protocol but ruining what would have been a superb finale to the series.
England and Wales Cricket Board chairman Giles Clarke said on Sunday he would be lobbying for a rule change regarding light, effectively putting the decision back in the hands of the batting side, and Flower feels just as strongly on the subject.
"Where I think the ICC (International Cricket Council) could improve the regulations - and we have spoken with their officials about this for years - is the description that they use when judging bad light," Flower said.
"They say they consider if it is dangerous or not. It is often not dangerous, it's a poor description of that particular regulation.
"It my opinion it is whether the battle between bat and ball is reasonable and fair.
"If there are spinners bowling under the regulations at the moment it is almost possible to play until it is dark because it is obviously not dangerous.
"They do need to change the regulations. Cricket will be better for it."
England's indignation over a decision that denied them the chance to press for their first ever 4-0 Ashes win on home soil was shared in Parliament.
Minister for Sport Hugh Robertson, who was among the disappointed fans at the ground, slammed the decision to deny the game a natural conclusion.
"I was at the Oval yesterday and the scenes at the end were farcical. With only four overs remaining in the flagship cricket series in front of a packed house, common sense should have prevailed," he said.
"I support the ECB's move in making strong representation to the ICC to get the rules changed."
The Ashes: Andy Flower plays down talk of England exit
Advertisement