Nigel Mawer, head of the WPBSA's Integrity Unit, will make enquiries to establish the events surrounding the PTC3 match at the South West Snooker Academy featuring Davis and Thepchaiya Un-Nooh on September 8.
Davis beat the Thai player 4-0.
WPBSA chairman Jason Ferguson said: “The WPBSA has a network of international partners to monitor such issues. We take any potential breach of the Members Betting Rules very seriously.
"Any player found guilty of such a breach is likely to be banned for life from snooker. Protecting the integrity of the sport of snooker is of paramount importance."