With Andrew Flintoff out for three months with an ankle surgery, Strauss is expected to be appointed for the five One-dayers against Pakistan and October's ICC Champions Trophy.
And Fletcher has hinted that England may rethink their decision to declare Flintoff as their captain for the Ashes in November.
"Andrew has captained very well in the sense that he has started with a new side," said Fletcher.
"It wasn't easy for him going through that loss to Sri Lanka but he is a really strong character and nothing has highlighted that more than the fact that being captain hasn't really affected him.
"Secondly he has got hundreds in the second innings twice against Pakistan, which is the hardest time to get hundreds."
When the extent of Michael Vaughan's absence was made clear earlier this year, it was announced that Flintoff would lead the side indefinitely.
However, the Lancastrian talisman has played just three Tests this summer and is not due to regain match fitness until shortly before the first Test in the Ashes defence in Brisbane on November 23.
"That is the kind of thing we have to keep in house amongst the selectors," Fletcher said of the captaincy conundrum.
"Every time we meet we debate certain positions but at this stage we have spoken about Freddie being a natural leader in Australia and we will have to talk more when the time comes."
Meanwhile Nottinghamshire wicketkeeper Chris Read increased his chances of being first choice behind the stumps this winter with solid contributions in this week's 167-run win over Pakistan at Headingley.
"Chris Read did very very well because he was under two types of pressure," said Fletcher.
"In the first innings he was under personal pressure to come back in and handle the expectations, which wasn't easy - he responded by getting that useful 38.
"But the biggest thing for him was in the second innings when he had to hold things together against those bowlers bowling reverse swing with inconsistent bounce.
"Danish Kaneria was also causing problems so he had to hold that tail-end unit together, because they are really inexperienced, so his 55 was probably worth a lot more than that."