"I don't think there is any question he won't be in charge this summer and beyond," Finn told BBC's Sportsweek.
Trott added: "I don't see anyone else captaining England - well, not for a couple of years."
The 75-run defeat in Galle was England's fourth in a row following the
3-0 whitewash by Pakistan
in the United Arab Emirates earlier this year.
Strauss's 110 against Australia in the
first Ashes Test
in Brisbane in November 2010 is his only century in 48 Test innings. He is averaging just 25.4 - compared to his career average of 41.2 - in four Test matches this winter.
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