Former England captain Nasser Hussain has urged the ECB to do everything it can to bring the “meticulous” Flower back on board.
One potential obstacle is that Flower is currently in charge of IPL franchise the Royal Challengers Bengaluru.
‘Progressive’
But Gould, who insisted he had yet to have conversations with Flower or any other potential successor to McCullum, said the ECB was open to a possible job-share arrangement.
“I think you’ll find that we need to be progressive in these issues,” Gould said.
“Where we have players trying to balance between county, franchise and international cricket, we may have to do the same with our coaching staff and support staff, but that is something we’ll have to have a look at.”
Gould said an interim appointment may be needed for the upcoming three-test campaign at home to Pakistan, although his preference was to have a fulltime coach in place for a series opener at Headingley, starting on August 19.
“Ideally, we’ll have someone in place for the Pakistan test, but that also clashes with other franchise tournaments and international fixtures around the world,” Gould said.
“Therefore, if we need to take a little bit longer to get the person we want, we’ll take that time.”
McCullum’s exit has followed the international retirement of former England test captain Ben Stokes.
But England managing director Rob Key remains in place, despite vocal criticism from 2005 Ashes-winning captain Michael Vaughan.
Key has come under fire for overseeing a sharp decline in test results and for his handling of several off-field disciplinary problems, which led to new guidelines on alcohol being sent to England players last week.
But the former England batter received staunch backing from Gould this morning.
“He has got a really good brain,” he said.
“He is a good communicator, he has got extraordinary knowledge of what goes on within our game in England and he has spent the last four years in one of the most difficult jobs in English sport.
“None of us are immune to results, whether it is coach, captain, director of cricket or chief executive.
“The key is [that] whatever changes we make, they are the ones most likely to bring the most rapid resolution to results we want.”