The world no.2 and four-time champion lost the Italian Open final to no.16 seed Alexander Zverev 4-6, 3-6.
Djokovic produced his best tennis to beat no.8 seed Dominic Thiem 6-1, 6-0 in just 59 minutes on Saturday evening.
Nole moved into the last four of the Italian Open on Saturday as he beat Juan Martin del Potro 6-1, 6-4 in their delayed quarter-final match.
The second seed continued his run at the Internazionali BNL d’Italia, defeating Roberto Bautista Agut 6-4, 6-4, en route to the last eight.
Novak improved to 3-0 against British qualifier Aljaz Bedene in their H2H series on Tuesday at the Internazionali BNL d’Italia in Rome.
The last of three ATP World Tour Masters 1000 events contested on clay takes place in the capital of Italy from May 14-21.
The world no.2 and two-time champion lost to no.4 seed Rafael Nadal 2-6, 4-6 in one hour and 38 minutes.
Kei’s withdrawal sends the defending champion into last 4 where he will face Rafael Nadal (ESP, 4).
Novak recorded a 6-4, 7-5 victory over Feliciano Lopez in one hour and 33 minutes on Thursday.
Nole goes on to play Feliciano Lopez (ESP, H2H 8-1) in the last 16 on Thursday.