Hong Kong's South China Morning Post reports the attendant said she wanted to throw the drink at Paetongtarn, one of Mr Thaksin's three children and the niece of current Prime Minister Yingluck Shinawatra.
"I immediately told my flight manager I could not work knowing the daughter of my enemy was on the plane," the attendant reportedly posted on Facebook.
"I called my personal adviser asking if it would be all right to throw coffee at Paetongtarn, but was told that this could breach Hong Kong's laws."
The Hong Kong flag carrier said they were investigating "allegations of misconduct" following the November 25 flight from Bangkok to Hong Kong.
Reports also said the attendant posted a photo of the manifest for the flight Paetongtarn was on.
"Cathay Pacific regrets this unfortunate incident and wishes to assure all of our customers that their privacy -- and strict adherence to all privacy regulations -- is extremely important to us," a Cathay spokeswoman said.
The airline said the attendant -- which it declined to identify -- is cooperating in the investigation and "is currently not operating", but would not confirm whether she has been suspended from duty.
Thai media quoted Paetongtarn as saying on social media that she felt "uncomfortable" after the incident and that she was travelling to Hong Kong for a business trip and to see her father.
The long-running political crisis in Thailand recently saw its first major street protests against the government of Prime Minister Yingluck Shinawatra, Mr Thaksin's younger sister, who is accused by her rivals of being a puppet for her fugitive brother.
Mr Thaksin, ousted in a military coup in 2006, has been living abroad to avoid a jail term for corruption, but makes regular visits to Hong Kong, the southern Chinese city where his family reportedly owns properties.