Britain want to work again with ace Cook.
The 21-year-old European champion was ranked first by the World Taekwondo Federation in the under-80kg category, but Lutalo Mohammad was instead selected by British Taekwondo for the London 2012 squad, leading to a drawn-out process which was eventually ratified by the British Olympic Association.
Mohammad went on to win the bronze medal, while Wales teenager Jade Jones claimed gold in the women's 57kg category and Liverpool's Martin Stamper reached the semi-finals.
Cook, who left the Manchester-based GB Taekwondo Academy training programme in the run-up to the Olympics, feels it is impossible for him to work again within the current Team GB set-up.
Manx athletes compete under the GB flag at the Olympics but, according to Cook, the World Taekwondo Federation (WTF) may introduce a route to future Games based on rankings rather than discretionary selection which saw him miss out this year.
GB Taekwondo performance director Gary Hall has always insisted the governing body remain willing to build bridges and have written to the 21-year-old martial arts star, who fought at the Beijing Olympics, to express their desire for positive talks.