England: Mickey Arthur, Ottis Gibson & Gary Kirsten in frame for coach's role
Pakistan coach Mickey Arthur is one of the names being considered as a replacement for England coach Trevor Bayliss when he leaves at the end of the summer.
On Monday, England director of cricket Ashley Giles said he had informally sounded out candidates.
South African Arthur, who has also coached his home nation and Australia, has been spoken to.
He is known to be interested in the job, confirming as much in July.
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Arthur has tasted success in the UK, having been in charge of South Africa when they won a Test series in 2008, and again when Pakistan won the Champions Trophy in 2017.
Australian Bayliss has opted to leave England when his contract expires after the Ashes.
Despite the heavy workload placed on England coaches, the intention is for his successor to preside over all three formats.
That potentially narrows the list of options, with many coaches preferring short-term roles in Twenty20 leagues, rather than an intensive international schedule.
Australian Andrew McDonald has been linked to the job, but told Test Match Special on Thursday: "With the franchise game, you get the opportunity to work with the best players in the world and spend less time away from home.
"The excitement of the franchise space outweighs the grind, taxation and time away from the family."
When asked if he would be interested in the England job, McDonald, who will take charge of the Birmingham-based team in the new Hundred competition, said: "I've taken this job and declared my hand."
Other potential candidates are South Africa coach Ottis Gibson and former India coach Gary Kirsten.
West Indian Gibson has had two spells as England bowling coach and took charge of South Africa at the end of 2017.
With his Proteas contract due to expire, Gibson, who lives in England, said in May that he was "happy to be linked with any job".
Kirsten, the former South Africa opener, won the World Cup with India in 2011 and is currently in charge of Indian Premier League side Royal Challengers Bangalore.
In addition, current England assistants Chris Silverwood, Paul Collingwood and Graham Thorpe could be considered.
Giles has previously spoken of his desire to appoint an Englishman, but said that will come second to finding the "best bloke".
And, it could be that the job has come too soon for all of Silverwood, Collingwood and Thorpe.
There is a possibility that England will have an interim coach for the tour of New Zealand in November, but that would be less likely if they do promote from within.