Swansea were leading 1-0 in Sunday's Premier League clash at the Britannia Stadium when the hosts were awarded a controversial penalty as referee Michael Oliver adjudged Angel Rangel to have fouled Victor Moses inside the area.
Charlie Adam converted the resulting spot-kick before Stoke went on to win the game 2-1 through Jonathan Walters' second-half header.
Monk was clearly dissatisfied after the game, labelling the penalty a "disgrace" and "disgusting" before going on to accuse Moses of cheating.
On Thursday, the FA released a brief statement confirming they had got in touch with Monk asking him to further clarify his remarks.
"The FA has contacted Swansea City manager Gary Monk to seek his observations in relation to post-match media comments he made after Swansea"s game against Stoke City on 19 October 2014," it read.
"Monk has until 27 October 2014 to reply."
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