England captain Alastair Cook declined on Saturday to offer any assurances to mercurial batsman Kevin Pietersen about his Test future.
British media had earlier claimed Flower has threatened to quit if Pietersen, their leading run-scorer in the Ashes series, continued to be part of the team's rebuilding process.
South Africa-born Pietersen, 33, ruled out retirement and said he wanted to help England regain the Ashes in 2015 but Cook was non-committal about the future of England's fourth highest Test scorer of all time.
"It's only been a week since everything has happened. So what is important for me is the One-Day series at this precise moment of time," Cook told reporters ahead of Sunday's one-day series opener at Melbourne.
"We know that when we go home from this One-Day series, a lot of important decisions on how we go forward with the Test team, one day team, my future that kind of stuff."
Persistently asked about Pietersen's attitude, Cook said: "It's very hard for me to talk to you, the media, about stuff like this.
"It's very hard and I can't do that. Confidentiality and stuff like that means what happens in the dressing room, stays in the dressing room."
Told that it did not ring as a sound endorsement for Pietersen, Cook said, "You can regard that as you want. As is always the way with the media that's what happens."
England's Ashes campaign was badly hit when top order batsman Jonathan Trott abruptly returned home after the Brisbane opener to deal with a stress-related illness, necessitating a batting order rejig that did not click.
Compounding the crisis, frontline spinner Graeme Swann quit international cricket after England had surrendered the coveted urn after a hat-trick of defeats.
"Obviously when you lose a series five-nil, lot of things get thrown up and thrown in your face as the captain and you start looking at everything and it's important that we do that," said Cook.
"What also is important is it's only been a week since everything has happened. So what is important for me is the one day series at this precise moment of time."
Image: Kevin Pietersen and Alastair Cook