Opening batsman Perera had alerted the officials about an approach made by bookies to him and left-arm spinner Herath to underperform during the Test against West Indies at Galle in October.
Sri Lanka Cricket (SLC) sources also revealed that captain Angelo Mathews and team manager Jerry Woutersz are due to be interviewed by the FCID.
The FCID investigation began following a complaint lodged by the Sports Minister Dayasiri Jayasekera.
Jayasekera earlier said a practice net bowler in the national training squad and a coach are also being suspected of having links to match-fixing operators.
Sri Lanka lost their number one ranking in the ICC T20 ratings when they lost 0-2 to the home side.
They also lost the Test series by the same margin and the ODI series 1-3.
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