IAG agreed a €1 billion (£840 million) deal for the Spanish carrier in 2019, but this was later halved to €500 million (£420) owing to the effects of the pandemic.
The Competition and Markets Authority (CMA) has now stepped in, Reuters reports, and has set a 19 January 2022 deadline for an initial decision.
The European Commission is also investigating the deal, stating in June it was worried the arrangement could harm competition on dozens of Spanish domestic and international routes.