The Serbian will next face Austrian fifth seed Dominic Thiem with a possible quarter-final against defending champion Nadal, who plays Karen Khachanov in the last 16 on Thursday, up for grabs.
But Djokovic insisted he wasn't looking past the clash with Thiem, a French Open semi-finalist in each of the last two years.
"It's disrespectful towards Dominic and Dominic's tennis... To think about and talk about potentially a match-up with Nadal," Djokovic added.
"Last year in Roland Garros he beat me in straight sets. He's definitely (a) top-three player in the world on clay."
Djokovic came through a tight first set in a tie-break and moved a break clear in the second, before late drama as he tried to close out the match.
The 39th-ranked Coric saved two match points on his own serve with Djokovic leading the second set 5-3, before fighting back from 40-0 down as the former world number one struggled to get over the line.
A succession of wild backhands and a tame forehand into the net saw four more match points come and go, before Coric levelled the set at 5-5 as Djokovic blasted wide and long.
The ninth seed rediscovered his composure, though, to break again and finally complete the job at the 10th time of asking as Coric sent a backhand flying long.
Nadal started his bid for an 11th Monte Carlo title with a comfortable victory over Slovenia's Bedene.
The 16-time Grand Slam winner...