It follows an ongoing dispute between gymnast Thema Williams and the Trinidad and Tobago Gymnastics Federation, with the International Gymnastics Federation (FIG) handing TTOC a deadline of May 9 to decide whether to take up their spot.
TTOC's Games Management Committee met on April 29 and 30 to discuss their response to the matter.
Williams competed in the artistic women’s individual qualification at the World Gymnastics Championships in Glasgow last year, finishing 59th, ahead of her team-mate Marisa Dick in 77th.
As the top finisher from the country at the Championships, it was expected that Williams would represent Trinidad and Tobago at the Rio 2016 test event, a qualifier for the Olympic Games.
After the Championships, the country revealed they had not decided on their representative, while both gymnasts were referred to their Disciplinary Committee after semi-nude photographs were published online.
Eventually Williams was selected to compete at last month's test event only to be withdrawn by the team ahead of the competition due to apparent injury, with Dick selected as her replacement.
Dick went on to become the first gymnast from the country to book an Olympic place in gymnastics competition but Williams has disputed her withdrawal and has alleged a campaign against her.
She has indicated that she could take legal action in order to pursue a place at the Games.
"Thema has been nursing an injured ankle and has limited all pounding and landings for over the past week,” said gymnastics coach John Geddert before the test event.
He went on to claimed that "unfortunately she fell six times out of three events on podium training and has since showed no signs of recovery".
Geddert added: “We are sincerely concerned for her health and cannot risk further injury."
Williams refuted the claim and told guardian.co.tt: “It was not something that was surprising to all those who have been around me and experiencing all the things they tried and all the attempts they made to stop me, I am not surprised that it has come to this.”
FIG have confirmed that the Trinidad and Tobago Gymnastics Federation had a free choice in which gymnast to choose at the test event, while revealing a name change from Williams to Dick was made in line with FIG rules and within the time limit.
The governing body also expressed that as the place earned by Dick was nominative, no name change or replacement would be possible.
If a decision is not made by May 9, an automatic invitation will be given to the next best ranked athlete from the test event.