The comments may have fallen foul of Thailand's strict "lese majeste" laws, which relate to defamation against the country's revered royal family.
The remarks under investigation are understood to refer to prison terms handed down for application of the laws, or Section 112 of the country's criminal code.
The U.S. State Department said in a press conference that it was "aware" of reports of the inquiry.
"The U.S. government has the utmost respect for the Thai monarchy," spokesman John Kirby said.
"Ambassador Davies reiterated longstanding U.S. policy on the issue of freedom of expression."
The Bangkok Post quoted
an unnamed official from Bangkok's Lumpini police station, which has jurisdiction over the area that the FCCT is located in, confirming that officials are investigating.
"It's not yet a formal investigation as we're still in the process of gathering information and fact-finding. If we find the ambassador's remarks defamatory according to the law, then we will launch the official investigation," the official said.
The FCCT said the police have asked for its assistance.
"The Foreign Correspondents' Club of Thailand has been asked by the Thai Police to assist them in an official investigation into whether comments made by U.S. Ambassador Glyn Davies at the club on 25 November violated article 112 of the criminal code, the lese majeste law. The FCCT is cooperating with the police," Jonathan Head, President, FCCT, said in a statement to CNN Wednesday.
The speech, which Davies delivered at the FCCT's premises late last month, provoked nationalists to demonstrate outside the U.S. embassy a few days later, the Bangkok Post reported
Davies, a senior career diplomat who was sworn into the post in September this year, previously served as the Special Representative of the U.S. Secretary of State for North Korea and has a number of other ambassador-level postings.
International groups like Human Rights Watch have repeatedly criticized Thailand's tough laws against defaming, insulting or threatening the royal family.