The report, which ranks countries based on anti-trafficking efforts, matters to the government as it tries to fully normalise relations with Washington and to show it is tackling tough issues better than previous civilian administrations.
Last year, Thailand's status was upgraded a notch to the Tier 2 "Watch List". It had been downgraded to the lowest level, Tier 3, after the 2014 coup.
"We believe that any government would have a good feeling about, or even admire, what we have done," Mr Don told a news conference. "We certainly are hopeful we'll be viewed favourably."
In 2016, Thailand investigated 333 cases, prosecuted 301 people and convicted 268, he said. In the previous year's TIP report, Thailand reported investigating 317 cases, prosecuting 242 people, and convicting 241.
The government has vowed to crack down on human trafficking, particularly in the multi-billion-dollar seafood industry.
But rights groups say millions of migrant workers remain vulnerable to abuse in fishing, the sex trade and other industries.
Mr Don did not expect any change in US emphasis on the importance of fighting human trafficking under new President Donald Trump, but said it would remain a priority for Thailand anyway.
"We'll keep on as we have done," he said.
Thailand submitted its report on anti-trafficking efforts for the year 2016 to the US on Tuesday. The US State Department's TIP report usually comes out in June.