A source close to the group says "there is no bad blood" between the boys and they intend to get back together in the future.
One Direction will disband for a year in March to focus on solo projects, according to The Sun.
A source close to the boyband told the newspaper: "The guys have been together for five years, which is an incredible run for any boyband.
"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% behind the decision.
"It is definitely not a split and they fully intend to get back together at some time in the future."
It is reported that performances planned for the rest of the year are expected to go ahead and the band will regroup after Christmas to finish contractual commitments.
There will be no tour for the band's fifth album and their last concert will be in Sheffield in October.
News of the temporary split comes after former member Zayn Malik announced in March he was leaving the band to feel like a "normal 22-year-old" and to pursue a solo career.
In July he tweeted a photo showing him signing a new record contract with RCA Records. He tweeted: "I guess I never explained why I left, it was for this moment to be given the opportunity to show you who i really am! #realmusic #RCA !!"
The Sun quotes the source as saying the remaning members of the group - Harry Styles, Liam Payne, Louis Tomlinson and Niall Horan - were thinking about disbanding with our without Malik.
"This was the plan with or without Zayn," the insider said. "In fact, the band have been making amazing music and been incredibly happy without Zayn.
"Of course they would have preferred that he had stayed in the band, but they would have taken this extended hiatus even if he hadn’t left."
The Sun's head of showbiz Dan Wootton, who broke the story, told Sky News: "After five years together they're hungry to try something else.
"There is a lot of demand for Harry Styles to be a big solo artist and launch a Hollywood acting career and there is a lot of speculation that Louis Tomlinson will join the X Factor judging panel next year.
"Liam Payne and Niall Noran are interesting in pursuing their song writing careers."
Disappointed fans have been posting messages on social media expressing their dismay at news of the group's plans for an extended hiatus.
One Direction follower @incredible_ari tweeted: "no tour for the next album !?!! I haven't got the chance to see them live yet this is not okay. even if this is a rumour im still crying at the the thought. help."
Another fan, @chloeduncan, tweeted: "@onedirection if you split up then I will officially cry for the rest of my entire life."