"I don't know exactly what happened," the PM told the BBC.
"He's a constituent of mine, a friend of mine. He's a huge talent.
"Because he is such a huge talent and he amuses and entertains so many people, including my children, who'd be heartbroken if Top Gear was taken off air, I hope this can be sorted out, because it's a great programme and he's a great talent.
"Every organ has to be free to manage its talent. I don't want to interfere in the running of the BBC. I hope it can be sorted out.
"The prime minister has many responsibilities, sadly, securing the future of Top Gear isn't one of them."
Cameron and Clarkson are part of a group dubbed as "The Chipping Norton Set"
-- wealthy media, politics and showbiz individuals who live in the affluent part of central England known as the Cotswolds.
Clarkson was suspended for allegedly hitting a producer,
the BBC reported on Wednesday.
The BBC said Clarkson, one of the corporation's highest earners, had "a fracas with a BBC producer" in a statement released on Tuesday.
"Jeremy Clarkson has been suspended pending an investigation," they said. "No one else has been suspended. Top Gear will not be broadcast this Sunday." The BBC reported that the next two episodes, and possibly the third and final show of the series, will not be aired.
The BBC director-general Tony Hall said
that the incident is being investigated.
Using the hashtag #BringBackClarkson, which is trending worldwide, some Twitter users lamented that the show would not be the same without him.
Clarkson himself also took to Twitter, posting an apology (of sorts) to Labour leader Ed Miliband -- for knocking him down the news agenda.
He also retweeted a "suffering" fan.
"Save Clarkson?" his co-host James May tweeted. "Save empty cardboard boxes and off-cuts of string. They're far more useful."
But a "Sack Jeremy Clarkson"
petition is also doing the rounds, gathering 16,500 signatures so far. Some will be glad to see the back of him.
Former CNN host Piers Morgan, who has had a series of run-ins with the presenter, also waded in with a cheeky jibe.
This is not the first time that Clarkson has been at the center of controversy.
In May last year, the television presenter asked forgiveness
after using a racist term during a taping of the show.
Clarkson had mumbled the n-word while reciting a children's nursery rhyme, but that version of the take was never aired.
Last year, the BBC show hit the headlines when Argentina complained
about a "Top Gear" special filmed in the country in which the number plate H982 FKL was used -- interpreted by some as a reference to the 1982 Falklands War.
Top Gear was named as the world's most widely watched factual program in the Guinness World Record
2013 Edition book, with an estimated 350 million global viewers. The show is sold to 214 territories worldwide.
In a previous article on their website, the BBC said
"Jeremy Clarkson is not a man given to considered opinion."
In their statement, the corporation declined to comment any further.