Despite reaching the final of the Australian Open and the semi-finals of Wimbledon, Djokovic did not reach the quarter-finals of any of this year’s Masters 1000 events.
He won the last of his 24 Grand Slam titles at the US Open in 2023.
Qualifying for Turin would have given him a chance to win a record eighth title at the season-ending championships.
Instead, only Americans Taylor Fritz and Tommy Paul remain in contention to take the final two spots currently held by Frances Tiafoe and Rafael Jodar.
Djokovic had not failed to qualify when he was in good shape since 2017.
Tiafoe’s chances were taken away earlier on Wednesday when he lost 6-3 1-6 7-6 (11-9) to Frenchman Quentin Halys.
The Australian Alex de Minaur then failed to take advantage as he lost 7-6 (7-2) 6-3 against the Argentinian Tomas Martin Etcheverry. A course in Paris could have ensured De Minaur’s qualification.
Elsewhere, world number one Alexander Zverev and fourth seed Daniil Medvedev, both already qualified for Turin, were also beaten.
Zverev said he was “annoyed” by the reaction to his position as world number one following a straight sets defeat to Lorenzo Musetti, while Medvedev was beaten 6-4 6-4 by Peruvian world number 33 Ignacio Buse.
Fritz was on the verge of elimination, but managed a decisive tie-break in the third set to win 6-7 (6-8) 7-5 7-6 (7-5) against 78th-ranked Slovak Alex Molcan.
Earlier, Paul beat Spaniard Daniel Merida 6-1 6-1.
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