Umtiti's previous deal was due to expire in 2023 but by extending it over an additional three years without committing to paying him more money, Barca are able to significantly spread out how much he is paid each season.
"The French defender is reducing a part of the salary that he was due to receive in the year and a half remaining on his contract," Barca said in a statement confirming Umtiti's renewal.
"This contract extension operation does not entail any greater financial commitments for FC Barcelona with regard to the player.
Through this contract extension, FC Barcelona will be able to increase its 'financial fair play' quota and thus register @FerranTorres20 with the Spanish Professional Football League. https://t.co/M49mXejym3 pic.twitter.com/oJcFR8esbv— FC Barcelona (@FCBarcelona) January 10, 2022
"FC Barcelona wishes to publicly express its gratitude to Samuel Umtiti for his willingness and the affection that he has demonstrated towards the club.
"Through this contract extension, FC Barcelona will be able to increase its 'financial fair play' quota and thus register Ferran Torres."
With gross debt standing at over €1 billion and after registering losses of €400m last season, Barca's LaLiga spending limit was reduced to €97m for the campaign.
With their wage bill significantly higher than that cap, they are operating under restrictions which mean they can only spend 25% of any savings they make that -- be that by reducing wages or bringing in transfer fees.
Alemany said earlier this month they made an "exception" when signing Torres from City as they did so knowing they were unable to register him with LaLiga.
Coutinho's exit and Umtiti's renewal have now created room for Torres, but the club continue to work on other departures in the hope of being able to add more players to their squad this month.
Torres is unavailable for selection after testing positive for COVID-19. Barca hope he will return a negative test in the coming days and, if he does, he could feature in the Spanish Supercopa this week.