LGBTQ+ charity Stonewall insists Qatar should not host the Olympics with the country reportedly ready to bid for the Games.
Qatar, where same-sex relationships are criminalised, is said to want to deliver the Games in 2036, using the World Cup as a platform for its ambitions.
Many fans have encountered problems and had rainbow flags and other LGBTQ+ items of clothing confiscated when trying to enter stadiums at the tournament.
England and Wales also did not wear the OneLove armband in support of the LGBTQ+ community in their opening games after being threatened with sanctions by FIFA.
Liz Ward, director of programmes at Stonewall, told the PA news agency: “Sport has the unique power to bring people together as we cheer on our favourite teams and athletes.
“Everyone, including LGBTQ+ people, deserves to feel welcome and included at all major sporting events.
Like the current World Cup, being staged in the winter for the first time because of summer temperatures in Doha, any Olympic Games in Qatar would also have to be moved.
It would not be the first time as the 1964 Olympics in Tokyo were held in October while Seoul 1988 and Sydney 2000 started in September.