Surapong Tovichakchaikul said the passport could be returned as a “New Year’s gift”.
The previous government revoked his passport, accusing him of encouraging protests by his supporters in 2009.
Mr Thaksin lives in exile in Dubai and has travel documents issued by Montenegro and Nicaragua.
The former prime minister was overthrown in a coup in 2006 while he was out of the country.
He was later prosecuted for abuse of power and sentenced to jail, but he fled the country before the end of the trial.
However, parties linked to him won the most votes in both elections that have taken place since the coup.
Rumours have circulated that he could be on the way back to Thailand ever since the current government – led by his sister Yingluck – was elected in a landslide earlier this year.
Mr Surapong told reporters that the previous government revoked his passport without any order from the courts or police.
“So I will use my authority to do whatever is not illegal under the regulations of the ministry to give the passport to ex-Prime Minister Thaksin,” he said.
“We are checking some more details but it will be very soon.”