Morgan led the ODI side to home series wins over both Sri Lanka and Pakistan this season but, together with fellow batsman Alex Hales, decided against travelling to Bangladesh for next month’s series.
However, former England captain Strauss said the decision would not be held against the pair, with Morgan set to lead the one-day side on their subsequent tour of India.
“Right from the start we said there are not going to be any recriminations,” Strauss told BBC Radio on Sunday.
“It’s not like these guys are going to be blacklisted and their names will not be put forward for selection. They absolutely will be.
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“Both have done outstanding jobs for England over the last 12 months, especially Eoin Morgan whose captaining has been sensational.
“Of course, we can’t give any guarantees because the situation might change on the ground in Bangladesh.
“Someone might come in and do unbelievably well, but the intention is for Eoin to come back in as captain and Alex will be in the mix for selection as well.”
England’s tour of Bangladesh, which begins on September 30 and will include two Tests and three ODIs, was called into question after an attack on a cafe in Dhaka in July which saw 20 hostages killed, including 18 foreigners.
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However, the ECB gave the tour the go-ahead after an inspection visit to Bangladesh led by team security chief Reg Dickason.
Strauss was unhappy that Morgan and Hales were not prepared to accept Dickason’s assurances but respected how they had reached their respective decisions.
“They were both very mature in the way they went about this,” said Strauss. “They took everything in and didn’t rush into a decision, but ultimately it came down to them not feeling comfortable about going to Bangladesh.”
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