The band, who enjoy a massive global teenage following, did not comment when contacted by AFP and have not commented on the tabloid report on their various Twitter accounts.
"The guys have been together for five years, which is an incredible run for any boyband," said The Sun's source.
"They fully deserve to have at least a year to work on their own projects. There is absolutely no bad blood between them and they are all 100 percent behind the decision.
"It is definitely not a split and they fully intend to get back together at some time in the future."
Fans took to social media to express their shock, with Twitter user Lexie Noel posting that "I've never cried harder".
Bee @hellobee added: "WHAT IS THIS NEWS ABOUT ONE DIRECTION SPLITTING UP IM DYING IN THE GROCERY STORE OMG".
Battle-hardened fans offered advice to those going through their first boy-band split.
"It's ok One Direction fans, I went through this with Take That & Boyzone," wrote Twitter user @LisforLia
"You may feel like your heart is in a blender, but you can do this."
The band is due to release its fifth album before Christmas, and fulfil promotional commitments by the end of February, the report said.
There is no tour scheduled for the new album.
One Direction's last scheduled concerts are at the Sheffield Arena in northern England on October 29, 30, 31.
They are currently touring North America and are due to perform in Milwaukee, Wisconsin on Tuesday.
Put together for a British television singing contest in 2010, Niall Horan, Zayn Malik, Liam Payne, Harry Styles and Louis Tomlinson swiftly developed a giant, fiercely loyal following of young girls worldwide.
The chart-toppers have sold more than 50 million records around the globe.
Malik quit the band in March, shortly after being signed off with stress.
"I am leaving because I want to be a normal 22-year-old who is able to relax and have some private time out of the spotlight," he said at the time.
The Sun's report said the split would have happened regardless of Malik's departure.
The Sunday Times newspaper's Rich List 2015 reckoned the band members were worth £25 million each.
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"The guys have been together for five years, which is an incredible run for any boyband," said The Sun's source.
"They fully deserve to have at least a year to work on their own projects. There is absolutely no bad blood between them and they are all 100 percent behind the decision.
"It is definitely not a split and they fully intend to get back together at some time in the future."
Fans took to social media to express their shock, with Twitter user Lexie Noel posting that "I've never cried harder".
Bee @hellobee added: "WHAT IS THIS NEWS ABOUT ONE DIRECTION SPLITTING UP IM DYING IN THE GROCERY STORE OMG".
Battle-hardened fans offered advice to those going through their first boy-band split.
"It's ok One Direction fans, I went through this with Take That & Boyzone," wrote Twitter user @LisforLia
"You may feel like your heart is in a blender, but you can do this."
The band is due to release its fifth album before Christmas, and fulfil promotional commitments by the end of February, the report said.
There is no tour scheduled for the new album.
One Direction's last scheduled concerts are at the Sheffield Arena in northern England on October 29, 30, 31.
They are currently touring North America and are due to perform in Milwaukee, Wisconsin on Tuesday.
Put together for a British television singing contest in 2010, Niall Horan, Zayn Malik, Liam Payne, Harry Styles and Louis Tomlinson swiftly developed a giant, fiercely loyal following of young girls worldwide.
The chart-toppers have sold more than 50 million records around the globe.
Malik quit the band in March, shortly after being signed off with stress.
"I am leaving because I want to be a normal 22-year-old who is able to relax and have some private time out of the spotlight," he said at the time.
The Sun's report said the split would have happened regardless of Malik's departure.
The Sunday Times newspaper's Rich List 2015 reckoned the band members were worth £25 million each.
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