Fleming would inherit a side that saw its momentum falter after a breathtaking start to the McCullum era.
McCullum won 10 out of 12 Tests in his first year in charge but since then, England have lost 18 and won 17 of 37 Tests.
They have not won a multi-match series since December 2024.
It is unclear whether Fleming would be in position to lead England in the three-Test series against Pakistan, which gets under way at Headingley on 19 August, or wait until December’s tour of South Africa.
Assistant coach Marcus Trescothick and former skipper Joe Root, who led the side in Stokes’ absence in the second Test against New Zealand, could fill the roles of head coach and captain, respectively, on an interim basis., external
Harry Brook is the current England vice-captain and received “100%” backing from Stokes to become his successor.
However the 27-year-old, who leads the white-ball sides, was overlooked for the role earlier in the summer.
His involvement in a nightclub incident last winter, when he was punched by a bouncer on the eve of a one-day international, was a contributing factor in that decision.
In addition to Flower, former Australian head coach Justin Langer was also expected to be a top contender for the England role.
However, on a recent appearance on the Stick to Cricket podcast, Langer said he had not been contacted by the England and Wales Cricket Board (ECB).
Former England batter Jonathan Trott, Richard Dawson, Gareth Batty and Australians Tom Moody, Darren Lehmann and Ryan Campbell were among the other names linked to the role.
The decision to remove McCullum came after the ECB hierarchy spent time reflecting on the situation surrounding the men’s team, with the 4-1 Ashes hammering in Australia followed by a 2-1 home series defeat by New Zealand, including Stokes announcing his retirement during play in the third Test.
Former England and Kent batter Key was backed to retain his position following the Ashes and defeat by New Zealand. Key and a headhunting company conducted interviews with potential candidates.