The match, played in the Turkish resort of Antalya on Wednesday, ended 2-2 with all the goals coming from penalties.
"FIFA contacted us and requested a full report from the Bulgarian Football Union (BFU) and also said they would receive a report from the Estonian FA," a BFU official who declined to be identified told Reuters on Friday.
"We will provide full assistance to FIFA."
Earlier on Friday, BFU president Borislav Mihaylov told reporters: "We had some doubts about the refereeing in this match".
There is also confusion over which referee took charge of the game.
Official reports from the BFU and the Estonian FA say the referee was Hungarian Krisztian Selmeczi.
However, Hungarian referees' chief Laszlo Wagner and Hungarian media have indicated the referee was Selmeczi's fellow countryman Kolos Lengyel. Wagner said the three match officials involved would now be suspended.
"I'm shocked because we didn't receive a letter to allow these referees (Selmeczi, Lengyel and Janos Csak) to officiate at this game," Wagner told Bulgarian radio.
"I can say that these three will not officiate any more matches while I'm head of the commission."
On Thursday, Estonia FA spokesman Mihkel Uiboleht told local media that his organisation were told about "possible manipulation" ahead of the match.
"The friendly was organised by an agency with whom we will not work any more," said Uiboleht.
"We received information of possible manipulation even before the game as the same agency also organised the match between Latvia and Bolivia and there was the same scenario there."
Latvia beat Bolivia 2-1 in a game featuring three penalties in a friendly held at the same venue earlier on Wednesday.
