The 29-year-old defender was brought in by Marcelo Bielsa from Real Sociedad in the summer of 2020.
This season, Llorente failed to establish himself under Jesse Marsch and was sent out on loan to Roma in January.
Llorente made eight appearances for Roma before he was sidelined by a muscle injury suffered in April.
Leeds negotiated an option to buy clause in his loan deal, but according to Italian daily Corriere dello Sport, Roma will not trigger it.
Roma consider Llorente a good defender but deem Leeds price of €18m too high and will look for other less expensive options in the transfer market.
Llorente has a contract with Leeds that is due to expire at the end of June 2026 and is set to return to Elland Road for pre-season in the summer.
The 29-year-old centre-back has featured 59 times for Leeds so far in his career and it remains to be seen what lies ahead in the future for Llorente.