Cook was rejected for a place on the Olympic team for a third time by a five-man panel on Wednesday, who prefer rising star Lutalo Muhammad. Cook is not part of the British Taekwondo high performance system and is self-financed.
The organisation’s stance has previously been question by the British Olympic Association.
WTF secretary general Jean-Marie Ayer said: "We are extremely disappointed by the way in which British Taekwondo's selection process has been conducted and it is clear that the lack of a conclusive rationale has caused confusion.
"The manner of the selection is bringing our sport into disrepute among the UK media and major Olympic stakeholders due to a perceived lack of transparency.
"Our main concern is always that every athlete is given fair and equal consideration – their welfare must come first. We at the WTF have done our utmost to bring fair practices and transparency to our sport, and that is why we have committed to undertaking this review.
"People all over the world practise taekwondo because it represents sport in its purest form: an individual display of skill, speed and strength.
"It is essential that the WTF preserves that purity for its 201 member countries and 70 million practitioners with transparent and decisive governance."
Cook is a twice European champion, while Muhammad also won gold at last month's Euros. However he is unproven in Cook's welterweight division and will need to drop down the weights to compete.
Team GB officials even had a legal observer present at British Taekwondo's selection meeting as they consider whether to take the matter further.
It all leaves Cook looking increasingly isolated. He has written to BOA chairman Lord Moynihan, UK Sport's Sue Nicholls and Olympic minister Hugh Robertson to state his case - but none really have the power to intervene.
Cook's camp are also fuming after they were given less than 24 hours notice to attend the selection meeting and have refused to rule out further legal action.
Few emerge from this process with any credit, apart from Muhammad, who has been receiving hate mail about his selection.
And if, as is increasingly expected, his selection is rubber-stamped, few athletes on Team GB will be under more pressure to deliver this summer.
“Aaron is disappointed to hear that Lutalo Muhammad has received hate mail," said a statement on Cook's website.
"No real fan of Aaron Cook would send such mail. We have always stated that we see Lutalo’s involvement in this mess as being a direct result of the decision by the Performance Team of British Taekwondo to recommend Lutalo for selection – wrongly in our opinion.
"Like Aaron, Lutalo is also a victim. Lutalo is an athlete of immense promise for the future.
“We have only ever discussed facts. Lutalo’s record as a taekwondo athlete in the Olympic category of -80kg does not compare to Aaron’s. Lutalo has never won an international event in the Olympic weight category of -80kg.
"There was not one athlete in Lutalo’s -87kg victory at the European Championships who will be at the Olympic Games. Lutalo is not ranked in the Top 100 according to the Olympic ranking. Aaron won the European and Olympic test event in the -80kg Olympic weight category.
"Aaron has beaten seven of the top 15 of his Olympic rivals in their most recent fights and lost to one, whilst Lutalo has not beaten any of them.
"Aaron is ranked number one in the world and Olympic rankings because he is the best Taekwondo athlete at his weight class in the world. These are all facts, not opinion."
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