It was announced in a Cricket South Africa statement on Monday morning that Du Plessis will not be back in England to lead the tourists on Thursday, when his fellow batsman Dean Elgar will instead take the reins.
Du Plessis is to remain in South Africa with his wife and their first child, following a difficult birth, but indications are that he will be available by the time the series moves on to Trent Bridge.
South Africa practised without him at Merchant Taylors School on Monday, and afterwards Domingo was able to confirm that he has reapplied for his own position - due to become vacant next month when the 42-year-old's contract expires.
"I have forwarded my application form and I have gone through an interview," he said."Absolutely (I want to carry on).
"It's a fantastic honour to work with this team. I've loved my time with it and I hope I can continue.
"If not, it's in the best interests of the team. I've had a fantastic run and loved every single minute of it. It's not my decision - it's up to the board."
Domingo is back in England, having overseen South Africa's Royal London Series campaign and their group exit from the Champions Trophy before returning home after his mother was injured in a car accident.
He was equivocal about his perceived hesitation before reapplying as coach by the due date last month.
"It was before the closing date," he said."When (exactly) is not too important, just as long as it's before the closing date.
"I've always said you never know what's round the corner - it's a process that needs to be followed, and I've got to respect it."They need to decide if I'm the right guy to take the team forward. So be it."
He cited several factors in his decision.
"It was a whole host of things, obviously family life ... number two the performance of the team ... whether you feel you're the right guy to take the team forward, it's showing signs of improvement in all formats - and player support is massively important," said Domingo.
"The most important support you need is from your players. I've loved my time working with them, and obviously from the support they've shown they've enjoyed what we've offered the team. That is satisfying to hear."
South Africa team manager Dr Mohammed Moosajee earlier explained the circumstances which persuaded Du Plessis to delay his journey back to England.
"Faf's wife gave birth to their first child last week, but the difficult nature of the delivery has delayed his return to the UK," he said.
The second Test is scheduled to begin on July 14.
Moosajee added: "The mother and baby have settled at home, but (Faf) will be unable to make it back in time to take part in the first Test match.
"He will link up with the squad in the UK later this week."
Elgar, who led South Africa in their drawn warm-up fixture against England Lions which finished in Worcester on Saturday, will be taking charge in a Test match for the first time.
He is set to have a full-strength attack at his disposal thanks to key seamer Vernon Philander's recovery from an ankle injury.
Philander took a full part in middle practice at Merchant Taylors.
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