The Australian pair, alongside Gary Kirsten, are the frontrunners for the role according to the former captain
Nasser Hussain feels Ricky Ponting and Justin Langer, the recently-departed Australia head coach, are the leading candidates to succeed Chris Silverwood.
The 4-0 Ashes defeat in Australia signalled the end of Silverwood's tenure after two-and-a-half years at the helm.
Interim managing director Andrew Strauss, who has come in following the exit of Ashley Giles, will lead the search for a temporary replacement for the West Indies Test series and help make a permanent appointment.
Langer is newly available after resigning as leader of the Australia men's team following the rejection of a six-month contract extension.
He oversaw victory at the T20 World Cup and the thrashing of England earlier this winter and has experience of county cricket after spells at Middlesex and Somerset as a player.
"If you're taking on Ricky Ponting you better be a pretty good cricketer to say 'no, I think you got that wrong'."
"I think there are some very good candidates," Hussain told Sky Sports. "I don't think you have to rush into it.
"One thing Justin Langer knows is the weaknesses of the England side as he's just played against them.
"He will know where they need improving and can work on and see them very close up.
"He also knows English cricket really well. He knows Strauss really well, they are good friends and he is a top man.
"Langer would push some questions in that dressing room. Which is I think what they need.
Hussain captained England in Tests between 1999 and 2003 (Gareth Copley/Getty Images)
"Joe Root is a lovely guy but I don't know if he is someone to grind them down in their faces."
Leading the criticism of Langer's departure from Australia has been Ponting, who has enjoyed four successful campaigns in the IPL with Capitals.
Three times DC have qualified for the playoffs and they went all the way to the final in 2020, eventually losing to Mumbai Indians.
Hussain, in conversation with fellow ex-England international Rob Key, added: "The other candidate we both respect is Ricky Ponting.
"I see Ricky, work with Ricky, listen to Ricky, see what he does at Delhi and when I've been in a commentary box with Ponting I often leave going 'this lad knows his cricket, this lad is a real cricket brain'.
Gary Kirsten has previously interviewed for the England job and has publically expressed an interest in the role (Gallo Images/Getty Images)
"I think Ponting would do a lot of good things. The respect Ponting would have in any dressing room around the world.
"If you're taking on Ricky Ponting you better be a pretty good cricketer to say 'no, I think you got that wrong'.
"Gary Kirsten would be very good. There are some good candidates out there.
"I am not sure that there are that many good English candidates, unfortunately, and that is something that needs looking at."
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