The Serb's father Srdjan was filmed posing with Russian flags, including one with Vladimir Putin's face on it, at Melbourne Park after Djokovic beat Russia's Andrey Rublev on Wednesday.
Russian flags are banned at the tournament, where a man standing with Djokovic senior was also seen wearing a T-shirt with a "Z" on it, a symbol of Moscow's invasion of Ukraine.
Back on the tennis court, the 35-year-old Djokovic admits that his deportation last year because of his stance on Covid vaccines has fired him up.
Accusations this week that he exaggerated the extent of a hamstring injury have also irked him.
"I don't think that I lack determination," Djokovic, who is attempting to equal Rafael Nadal's 22 Grand Slam crowns, said ahead of his clash with the unseeded American Paul.
"But you could say that there is something extra this year," he told reporters.
"You could say because - as you mentioned, the injury, what happened last year - I just wanted to really do well."
Djokovic is hot favourite to win a record-extending 10th Australian Open and anything other than a decisive win over Paul will be a huge shock.
The 35th-ranked Paul is playing his first Grand Slam semi-final.
Khachanov v Tsitsipas
In the other last-four clash, tournament organisers will be keeping their eyes peeled for a repeat of Wednesday's scenes when Russian fans gathered and chanted pro-Russia and pro-Putin slogans following Rublev's defeat.
Karen Khachanov, the Russian 18th seed, faces Stefanos Tsitsipas at Rod Laver Arena.
Third-seeded Tsitsipas is hoping to finally reach Sunday's final after losing three times previously in the last four in Melbourne.
The 24-year-old is also hoping to win a Grand Slam for the first time.
But in Khachanov he faces a player who is into consecutive major semi-finals, having reached the same stage at the US Open last year.
The 26-year-old has largely gone under the radar until now.
"I think the first semi-finals which I did in the US Open, that gave me an extra boost and extra confidence to show where I really am and what I can do when I'm at my best," Khachanov said.
"And how can I be more consistent with that form.
"So I think all those things together, they push me to where I am right now."
