Llorente's positive test, on the back of one for team-mate Sergio Busquets, shows that the virus has spread within the squad - all now training individually in isolation - and that could open the door for Llorente's club-mate Rodrigo and others to be drafted into the squad.
Players testing positive for Covid-19 can be replaced in the squad, or return to it if they return a negative after 10 days of isolation.
Llorente will definitely not face Sweden, who have themselves suffered two cases, in Seville on Monday but all being well will be able to return for the June 18 game against Slovakia, also in the city.
Spain's situation is helped by the fact manager Luis Enrique surprisingly decided to select only 24 players for the tournament. Countries are allowed 26, three more than normal to provide greater flexibility in case of situations like this.
Rodrigo is one of six senior players, along with Kepa Arrizabalaga, Raul Albiol, Carlos Soler, Brais Mendez and Pablo Fornals, training in a separate bubble on stand-by. On Wednesday a further 11 were added from the under-21 squad that has filled in for the seniors during Spain's warm-up fixtures.
If Busquets or Llorente were withdrawn by 9pm on Saturday, a replacement could feature against the Swedes.
As a forward or attacking midfielder, Rodrigo is not a natural replacement for Llorente or holding midfielder Busquets, but certainly is an option to beef up the squad after a strong finish to the season which saw him score four times in his last four matches.
He also had the virus in the autumn, which experts believe will boost his immunity.
Games can be delayed by 48-hours should a team have fewer than 13 players available, but if a team is unable to fulfil a fixture within that time, the opponents will be handed a 3-0 victory.
Juventus winger Dejan Kulusevski and Bologna midfielder Mattias Svanberg have both contracted Covid-19 with Sweden.
The news is the latest setback in a season which had been difficult for Llorente, but which he looked to be coming out of.
The 27-year-old signed from Real Sociedad last summer but a series of minor muscle injuries prevented him making his debut until late February. From there he made 14 consecutive starts, impressing with the quality of his defending and passing before his season ended prematurely with another muscle niggle.
He was, however, fit enough to feature in the June 4 friendly against Portugal, where La Roja kept a clean sheet.
Rodrigo's season has also been disrupted, not only by that bout of Covid but also injury and the form of Patrick Bamford.
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