Specialist detectives are investigating if up to four League of Ireland matches involving the same club may have been fixed.
Mobile phones and documents are currently being examined after being seized at the club's training ground in the south of the country on Monday.
The search was carried out by members of the Garda Economic Crime Bureau (GECB) after gardai received a complaint from the FAI.
It is being investigated if games were intentionally lost by the one team after a large amount of bets were placed on the opposition team winning.
A large number of fouls and yellow cards in the games, which may have influenced the outcome of the match, are at the centre of the investigation.
Detectives are currently focusing inquiries on the club, but will also attempt to establish if there is an international involvement in the allegations.
A source said gardai are attempting to establish how many people may have been involved in the alleged match-fixing.
"It's too early to say how many people were involved and investigations are ongoing," a source said.
"The focus is on the betting against one particular team which was influenced by incidents on the pitch, such as fouls and yellow cards."
The FAI said it is aware of the latest developments and is awaiting a report from gardai.
On Monday evening, gardai said they were at a sports grounds which had been searched. A number of players and staff were spoken to during the searches, but no arrests have been made. The alleged offences include conspiracy to defraud and corruption.
The owner of the club did not respond when contacted for comment yesterday.
A statement issued by the FAI last night said: "The FAI can confirm it is investigating unusual betting patterns around the recent FAI Cup game between Sligo Rovers v Limerick FC.
"The investigation is along similar lines to the one currently under way into the First Division fixture between Shelbourne and Limerick in April.
"Both investigations were launched following the receipt of reports from Uefa to the FAI concerning unusual betting patterns around the two games."