The defending champion – chasing a fourth straight title in Melbourne – will face the 15th seed after seeing off Uzbekistan’s Denis Istomin 6-3, 6-3, 7-5.
I have a great relationship with him, a real friend relationship for more than 10 years
The Serb has won all six of his meetings against fellow 26-year-old Fognini, who had never progressed beyond the second round at this tournament before.
But Djokovic is wary of the Italian’s pedigree having surged up from 47th to 16th in the world rankings over the past year.
“Of course, I respect him. I have a great relationship with him, a real friend relationship for more than 10 years,” said Djokovic.
“He’s a clay court specialist, so that’s where he made his best results. But lately he’s been performing really well on hard court. Today he beat Sam Querrey who is a hard court specialist with a big serve and in form.
“I don’t take anything easy.”
Djokovic was in control for most of his encounter against Istomin but was forced to serve for the match twice in the third set as he claimed his 27th straight victory.
With uncertain weather around organisers closed the roof on Rod Laver Arena, a decision which Djokovic had no problem with.
“Yes [I would prefer the roof open]. I practiced with an open roof and think it’s always nice to have some fresh air,” Djokovic added.
“But it’s understandable. Before the match, the people from the organization approached me and showed me the forecast and said it was going to rain on and off.
“It was unpredictable and they couldn’t risk it so they should close the roof. It was fine.”
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