Benedict Allen, 57, was dropped in the area by helicopter three weeks ago as he set off to find the reclusive Yaifo tribe, but he has not been heard from since.
His most recent post on his Twitter page on 11 October read: "Marching off to Heathrow. I may be some time (don't try to rescue me, please - where I'm going in PNG you won't ever find me you know...)"
The father of three has no phone or GPS service but was expected back in Papua New Guinea's capital Port Moresby on Sunday for a flight to Hong Kong, where he was due to give a speech to the Royal Geographic Society.
His sister, Katy Pestille, told Sky News that it was the second time he had gone missing.
She recalled: "When he was younger he went from the mouth of the Amazon to the mouth of the Orinoco, through all this uncharted terrain. He was the first person to do that. It's a long, long way and he was absent for six months and missing for three, so we've been through all this before.
"Not knowing where he was for three months was really, really awful. This was when he was about 22. Our parents were alive then and it was agony at the time.
"We are just sitting and waiting and just hoping that he'll just walk out of a bush, which is what happened last time."
Mrs Pestille said that she was not worried about the tribe, as her brother had visited them some 30 years ago and wanted to "reconnect with them", with nobody else having visited the Yaifo since then.
She added: "Usually he gets on very well with the tribes. It's the other people hiding in the jungle - drug dealers, illegal loggers and people that don't want to be found - who are more dangerous."
On his website, Mr Allen, who is based in Bristol with his family, describes the Yaifo as "the remotest people in Papa New Guinea" and "one of the last people on the entire planet who are out-of-contact with our interconnected world".
He also said the terrain he must traverse to reach them was "treacherous".
He wrote: "Either I must paddle down river for a week or so - or enlist the help of the Yaifo, as I did last time; together we managed to achieve the only recorded crossing of the Central Range. So, if this website or my Twitter account falls more than usually silent - I'm due back mid Nov - it's because I am still out there somewhere.
"So, don't bother to call or text! Just like the good old days, I won't be taking a sat phone, GPS or companion. Or anything else much. Because this is how I do my journeys of exploration."
His agent Joanna Sarsby told the Daily Mail: "His wife Lenka has not heard from him, she is very worried.
"He would never miss something like the Hong Kong talk unless something had happened.
"He is a highly experienced explorer, very clever and resourceful and adept at surviving in the most hostile places on Earth, and he would never give up.
"He may not be a young man any more but he is very fit."
Ms Sarsby described the Yaifo as "possibly headhunters, quite a scary bunch".
She added: "I just imagine he might have been taken ill or is lying injured somewhere, perhaps with a broken leg, and maybe being helped by locals. He never takes a phone with him - he believes in living like the locals."
Mr Allen has previously completed the first documented journey the length of the Namib Desert and is the only person known to have crossed the full width of the 1,000-mile Gobi Desert alone with camels.(c) Sky News 2017: Explorer Benedict Allen missing in remote Papua New Guinea jungle