England lost a high-scoring thriller to India by seven runs in Mumbai to bow out of the T20 World Cup at the semi-final stage which shifts the focus back onto McCullum after a largely chastening winter.
A 4-1 defeat in the Ashes, where they surrendered the urn inside 11 days of cricket, brought attention to England's planning, tactics and culture, leaving McCullum in a tenuous position.
While his England and Wales Cricket Board employers are conducting a formal review into what went wrong in Australia, McCullum reiterated his desire to continue a role he first inherited in May 2022 when he took charge of the Test side before taking on limited-overs duties at the start of last year.
"I'm enjoying the role, I'm enjoying the role across all formats and I'd love to carry that on," McCullum told the BBC.
"I'm not saying it's a great job because it's a lark, I'm saying it's a great job because I'm working with some of the most talented players in the world with an organisation that is very well structured, well run and well supported by the fans.
"I feel like we've made some significant improvements across the various formats.
"Yes, we've missed some opportunities, but I think this team has a real opportunity over the coming years to continue to improve and hopefully finish what we started. I'd love to be a part of that."
Brook and McCullum have made England a daunting prospect in T20s with 16 wins in their last 18 matches before Thursday night and the Yorkshireman insisted the former Black Caps captain be allowed to carry on.
"I've said plenty of times he's the best head coach I've ever had," Brook said.
"The way he speaks to everybody, he's got an aura in the dressing room. Everybody looks up to him and the things he did in the game as a player was unbelievable and he's just carried that into his coaching.
"One hundred and 25 per cent (he should stay on)."
India made 7-253 with Sanju Samson scoring 89. England fell just short despite Jacob Bethell registering his T20 best with 105 off 48 balls.
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