Sampson was sacked last week, a day after leading his team to a 6-0 win over Russia, for “inappropriate and unacceptable behaviour” in his previous role as manager of Bristol Academy.
The FA board met at Wembley on Monday for the first time since the furore surrounding Sampson flared up.
“A number of questions were raised around the historic processes which the board has asked the executive to look into further with the appropriate external legal support,” the FA said in a statement.
“The board is confident that, consistent with the substantial positive change under the leadership of (chairman) Greg Clarke and Martin Glenn, the right procedures are in place to prevent a similar issue arising now or in the future.
“The board also discussed ways to continue to improve support for England women’s teams and will consider recommendations on this when they next meet.”
Sampson’s behaviour was the subject of a year-long safeguarding investigation which started in March 2014, shortly after his appointment as England boss.
Based on an anonymous tip-off about a relationship with a teenage player at Bristol, the FA investigation cleared Sampson from a safeguarding point of view, but the 34-year-old was made to complete an education and mentoring course to address the player/coach issues raised.
All of this was detailed in a report the FA says nobody outside its safeguarding team read until 10 days ago, when another tip-off came that Glenn should reexamine the case.
Having done so, the chief executive’s response was swift but questions were asked about Glenn’s own position as he has admitted to not asking more questions about the safeguarding investigation until recently.
Sampson has been the focus of bullying and racism allegations for at least a year.
The FA said these claims had been investigated twice, once by an independent barrister, and Sampson had been cleared. He has also strongly denied the allegations.
But with the Professional Footballers’ Association dismissing the investigations as a cover-up, Glenn and his senior colleagues have been summoned to appear before lawmakers at the House of Commons Digital, Culture, Media and Sport select committee next month to explain their handling of the Sampson saga.
In a statement, committee chairman Damian Collins said: “Following the sacking of the England women’s coach, Mark Sampson, the Football Association must explain why it took so long to look into issues raised about the coach’s past.”