Flower ended his five-year tenure as England's team director on Friday, and Newell has been one of the coaches tipped to replace the outgoing Zimbabwean.
"I would be interested to see what the position is going to be as and when it is advertised," the 48-year-old told BBC Radio Nottingham. "I will take some interest in what happens with it over the next few days and weeks.
"My style is management as much as coaching and that seems to be the way England have run things in recent years.
"I would like to think I can do it in the future at England level."
Newell has been in his current role with Nottinghamshire since 2002.