Former Lilleshall-based coach Liz Kincaid has strongly denied all the allegations, according to a BBC report.
British Gymnastics had removed her from the team after an allegation was made about the mental health of one of her former gymnasts.
Retirement from the sport had been given as the official reason for her withdrawal before last year's 2020 games.
British Gymnastics said the British Olympic Association's rules state no-one with "any unresolved ongoing complaints about them" could attend the Games.
The BBC said that a wider independent investigation into allegations of abuse within British gymnastics is ongoing, after a number of current and former gymnasts alleged mistreatment at all levels of the sport in 2020.
The final report of the independent review, led by Anne Whyte QC and co-commissioned by Sport England and UK Sport, is due to be published at the end of May.
The BBC reported a number of allegations against Kincaid who said: "To suggest I would mistreat the gymnasts goes against every principle I live by and is very upsetting."
There is an ongoing investigation into the sport and two gymnasts as part of a civil claim against British Gymnastics, plus a legal claim raised by 37 former athletes who say they were victims of alleged systemic physical and psychological abuse at British Gymnastics.
British Gymnastics said in a statement: "There is no place for abuse of any kind in gymnastics and we are committed to working with anyone who makes a complaint to ensure their concerns are properly investigated and those proven to have been responsible for any wrongdoing are appropriately dealt with.
"British Gymnastics is determined to learn from all those who have bravely come forward and raised concerns. We are deeply sorry to those that have had a poor experience in our sport where we have fallen short. We are embarking on a comprehensive programme of reform to make positive changes across the sport, and we will be outlining these areas in much more detail once we have had the opportunity to study the Whyte Review and incorporate its recommendations fully into our reform plan.”