Joe Root and Stuart Broad could be future England Test cricket captains
"There are a number of players playing informal and formal leadership positions, and it's right that we have conversations with all those guys," said Strauss, suggesting he is open to ideas on candidates for the job.
But who will be knocking on Strauss' door clutching a CV with ambitions of taking over the toughest gig in English cricket?
Joe Root, England cricket captain?
Joe Root is the overwhelming favourite.
The Yorkshire batsman is the envy of every coach as one of the world's most talented cricketers and has already been Alastair Cook's vice-captain.
The role has seen him running the show when Cook has been off the field, the most extended period coming when the skipper was sent to hospital during a Test match in June for a scan on his knee.
The only reservations held about the 26-year-old are those around his other leadership experience – his swift promotion to Test cricket four years ago means he has rarely had the opportunity to captain at the highest level in domestic cricket.
Joe Root has proved an able vice-captain to Alastair Cook
"I think he's done a very good job as vice-captain," Strauss said.
"He's obviously matured a lot over the last couple of years or so and there's absolutely no reason why he won't be one of the strong candidates for the role."
Stuart Broad, England cricket captain?
Stuart Broad is no less fiery than he was when he made his international debut at the age of 20.
Stuart Broad captained England at the World T20 in Sri Lanka in 2012
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However, the fast bowler is far better at restraining and harnessing his rage for good as opposed to evil.
Broad, 30, has already worn the (notional) armband too. In 2014, he led England on an ODI tour of the West Indies, where England won 2-1 and spent three years and 27 games as T20I skipper.
The seamer is probably closer to retirement than his debut but he would still represent a captain who commands the respect of the dressing room and has enough experience to navigate international cricket.
Jos Buttler captained England in Bangladesh this winter
That said, the last time England went to Australia with a bowler in charge, it didn't end well (see Andrew Flintoff, 2006/07).
Jos Buttler, England cricket captain?
Initially, Jos Buttler looks a left-field choice. But the more you think about it, the more justifiable it is.
One of the most exciting ball-strikers around, Buttler is feared the world over as a man who can clout any bowler over the boundary – repeatedly.
He made an impressive return to the Test side in India with a fine 76 in Mumbai after more than a year out of the side.
The Somerset wicketkeeper, who played as a specialist batsman in the Tests, also deputised impressively by leading the ODI side in Bangaldesh this winter when Eoin Morgan declined to tour.
Even so, his leadership credentials are a little limited and he only has 18 Test caps, but if England really want to break the mould and pick a leader for their new generation, they should look no further than Buttler.
Could Jonny Bairstow balance captaincy with wicketkeeping?
Jonny Bairstow, England cricket captain?
Alec Stewart was the last wicketkeeper to captain England in Test matches but Jonny Bairstow is a very different character from Surrey's finest.
England have committed to his glovework despite initially picking him as a batsman and the work he has done with coach Bruce French has seen him drastically improve behind the stumps.
It looks a lot more natural to him and his batting does not seem to have suffered.
The question of whether he could handle the triple pressure of batting, keeping and captaining therefore seems academic as there is little this 27-year-old from Bradford can't do.