Clarkson was on a break with his family after shooting his Amazon Prime show with co-hosts Richard Hammond and James May, when he fell ill. He had planned to return to work after his holiday.
Clarkson's daughter Emily wrote his weekly newspaper column, published yesterday.
An insider said: "He's told friends not to expect to hear too much from him over the next few weeks which is very unlike him, and obviously his family are concerned," according to The Sun.
The source added: "Inevitably people close to him are saying it's time to think about the way he looks after himself - cutting back on the booze and fags - but he's never been one to take that sort of guidance on board."
A spokeswoman for The Grand Tour said: "Jeremy Clarkson was admitted to hospital on Friday morning during a family holiday in Spain, and is being treated for pneumonia."
This is not Clarkson's first health scare. In 2015, two days before assaulting a BBC producer, he was told by a doctor that he might have cancer.
Speaking in detail about the incident that resulted in his sacking from the Top Gear show, Clarkson said being given the warning was one of the most stressful experiences of his life.
In an attempt to explain his state of mind at the time of the attack, he said: "Two days before the "fracas", I had been told, sternly, by my doctor that the lump on my tongue was probably cancer and that I must get it checked out immediately. But I couldn't do that.
"We were in the middle of a Top Gear series. And Top Gear always came first."
Clarkson said he had now been given the all-clear, but wrote in his column in The Sunday Times: 'That was the most stressful day I have ever had in 27 years at the BBC.
'It was beyond-belief stressful, everything was gong wrong, and then you know... there you go. But everyone has stressful days, and they manage to cope better than I had.'
Clarkson was sacked by the Corporation after an "unprovoked physical and verbal" attack in Hawes, North Yorkshire that left his victim, Oisin Tymon, 36, in need of hospital treatment.
The presenter said the show about cars had come to dominate his life after his divorce from wife Frances and the death of his mother Shirley, and he worried about all parts of the programme.
The hospital incident comes two months after Hammond was airlifted to hospital when his car crashed while filming The Grand Tour.
The TV presenter, 47, was driving an electric super car in Switzerland when it crashed and burst into flames.
Hammond escaped the crash, which left the vehicle scorched and on its roof, with no serious injuries.
MailOnline has contacted Clarkson's representatives for further comment.
