The German investigation earlier identified a further discrepancy with the official online record of Djokovic's test, a timestamp for which indicating the corresponding web page may not have been created until December 26.
Djokovic, who has admitted breaking quarantine rules by carrying out an interview with a journalist on December 18, had left Serbia for Spain shortly after Christmas before flying to Australia via Dubai.
Representatives of Djokovic and the Institute of Public Health of Serbia have failed to respond to repeated requests for comment on the discrepancies with his test and whether they were merely glitches.
Asked whether the tennis authorities needed to get to the bottom of the matter, McEnroe said: "In short, yes. I'd like to know.
"I'll give you an example of something I don't understand. Novak Djokovic, to me, is an extremely smart person. If he tested positive on – what date is it? – December 15th – I'm throwing in a date – why in the hell would he do an interview with a journalist on December 16th?
"That makes absolutely no sense to me. The guy's not stupid. He's smart. So, already, I'm like, 'What?!'
"I mean, he wasn't just sitting around going, 'I hope I get Covid so I can get an exemption'. So that wasn't happening."
McEnroe, a pundit for Eurosport at the Australian Open, warned that the Serbian authorities would not investigate the matter themselves amid anger in Djokovic's homeland over his deportation.
Speaking on the day the 34-year-old was declared an honorary citizen of Budva, Montenegro, in one of his first public appearances since he was thrown out of Australia, McEnroe said: "I don't think that you'll be getting the Serbian authorities to try to figure out a way to make Novak look bad, if that's what anyone's thinking. That ain't happening."
The International Tennis Federation and Association of Tennis Professionals did not respond to requests for comment on whether they would investigate Djokovic's test.