The Test starting Sunday in Dhaka is the first between Australia and Bangladesh since Ricky Ponting's side toured the country in 2006 and claimed the series 2-0.
Bangladesh -- which only attained Test status in 2000 -- have moved on from that defeat, and hope to build on recent stronger form to impress fans with a series win on home soil against Australia.
"I don't see why it can't be possible. Our expectation: winning both Tests," Shakib told reporters in Dhaka.
"We need to do well in all aspects if we want to win the Tests. Whatever the strengths they have, Australia are always tough opposition. They can adapt to any conditions very quickly. None can do this better than the Aussies."
The visitors trained in Darwin, a tropical city in northern Australia, ahead of the Bangladesh tour to adjust to the hot and humid conditions expected for the two-Test series.
But even once touching down there were hiccups, with batsman Glenn Maxwell suffering heatstroke during an early training session and a warm-up match cancelled due to flooding.
Shakib said Bangladesh would be hoping to capitalise on Australia's poor run in recent South Asia clashes.
The world number-two Test side lost 3-0 to Sri Lanka in a series in 2016, before succumbing 2-1 against India earlier this year.
Bangladesh meanwhile have won two of their last three Tests, one against Sri Lanka and a historic win over England.
Shakib -- the world's top all-rounder in all three cricket formats -- said Bangladesh's spin attack would put pressure on the Steve Smith-led side.
The hosts are hoping Shakib, off-spinner Mehedi Hasan and left-arm spinner Taijul Islam can undo Australia's formidable batting lineup.
"I think our spin attack is better than them. I won't say in all conditions, but in our condition we are better than them," said Shakib.
"Taijul and Miraj (Mehedi) are bowling well for a long period. I hope they will do well in this series as well."
Shakib, Mehedi and Taijul took all 20 wickets when Bangladesh recorded their first-ever Test win over England by 108 runs in October.
The second Test of the series will be held in Chittagong from September 4-8.
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First Published: August 25, 2017, 9:12 AM IST