The 68-year-old is said to "deeply regret" signing up to appear on the ITV programme, after realising he doesn't fit in with the other contestants.
Could Michael Buerk be the third celeb to quit the jungle?
"Just as things were settling down, now Michael wants to go," a source told the newspaper. "Frantic efforts are being made to persuade him to stay.
"He adds a certain gravitas to the camp atmosphere. He would be a huge loss."
Michael's wife Christine is currently in Australia, waiting to greet him when he leaves the show – and she recently spoke to the Mirror about his appearance.
"He was low-key at the beginning, quieter than at home," she said of the journalist, who has formed an unlikely friendship with rapper Tinchy Stryder. "Michael likes his own company so it has taken him a while to settle in.
Michael Buerk pictured with his wife Christine
"But the last programme I saw he was getting into the group dynamic. You are seeing more of the real Michael now."
It was TOWIE star Gemma Collins who was the first to exit the jungle, after just three days. Her 72 hours were certainly eventful though; from her panic attack on the helicopter, to complaints about jungle food to her malaria self-diagnosis.
Shortly afterwards, Coronation Street star Craig Charles returned to the UK after being given the news that his brother had sadly passed away.