The new so-called “Super” Club World Cup will be played in China in June 2021 and will feature more teams than previous editions. For European teams to qualify, they need to have won either the UEFA Europa League or the UEFA Champions League in the 4 years prior.
Atlético have won the Europa League and Real the Champions League, but Barcelona have not won either in that time period. They could still win either one, but they have limited chances until the tournament starts - just two years.
Eight European teams will take part, the champions of the Europa League and the Champions League from 2018, 2019, 2020, and 2021. That would be Real Madrid, Liverpool, Atlético, and Chelsea in 2018 and 2019. Four spots are left open for 2020 and 2021.
In addition, South America will have six teams, while Africa, Asia, and CONCACAF (Central and North America, plus the Caribbean) would have three each. Last of all, Oceania would have one representative.
At present, each confederation typically sends one team for a tournament held annually at the end of the calendar year, with the hosts getting one spot as well for a total of 7 teams. The new version of the tournament, by contrast, would have 24 teams and be played only once every four years, replacing the FIFA Confederations Cup in the summer.
In case there were repeat champions, the next highest ranked team in the continent’s ranking would take a spot. As things stand, Barcelona are ranked #3 in the UEFA Club Coefficient list, but that, behind Atlético and Real. Meaning, if the ranking stayed the same, Barcelona would be able to take a spot if there was one repeat winner of either the Champions League or Europa League in the next two years, even if they did not win either competition. However, again, none of these factors are assured at all.