The Foreign Correspondents' Club of Thailand, which hosted Glyn Davies' talk, confirmed it is assisting authorities in their probe.
In it, Mr Davies expressed concern about the long jail sentences for violating the lese majeste law.
Those convicted of insulting the king, queen, heir or regent face up to 15 years in jail on each count.
Two people were recently given sentences of 28 and 30 years each for comments posted on Facebook.
Mr Davies' speech on 25 November at the club's premises in Bangkok touched on a broad range of topics, including King Bhumibol Adulyadej, whom he praised.
He said the US was concerned about the "lengthy and unprecedented prison sentences handed down by military courts" in lese majeste cases, and stated the US view that no-one should be jailed for peacefully expressing their views.
Mr Davies has diplomatic immunity from arrest. The Bangkok Post quoted a police spokesman as confirming that the authorities could not proceed with any legal action against the ambassador. But Thailand can rescind his diplomatic credentials.
The ambassador had only arrived in Thailand in October to take up the post.
A spokesman for the US embassy in Bangkok told the BBC that it was preparing a response on the matter.
Prosecutions under the law have soared since the military coup in 2014, with about 100 people charged. Critics say the law has been used suppress dissent.
Another ambassador in hot water with the Thai authorities is British envoy Mark Kent, over a tweet he posted three days ago.
In it, he contrasted the military government's tolerance of protests outside the US embassy against Glyn Davies by ultra-royalists with the detention of dozens of activists heading to protest at a military-built park glorifying Thailand's monarchy, which has been tainted by a corruption scandal.
"It is disappointing that the ambassador took a position that has supported a group that has often broken the law and disrespected judicial processes," government spokesman Maj Gen Werachon Sukondhapatipak said.
The foreign ministry says it was studying the British ambassador's comments to determine whether he should be summoned to receive a formal complaint.
The US ambassador to Thailand is being investigated for royal defamation over a speech he made in November.