|One Direction performs on NBC in New York|
A source close to the band told the Daily Star newspaper: "The offer was enormous and even tied into a safe sex organisation in the US. It came from one of the biggest brands in the world.
"While the boys didn't sneer at the money, they felt their fans were slightly too young for this type of project.
"They are promoting dolls and games, so that is the age group who are buying their products.
"The boys remain very candid about supporting the use of condoms if asked in interviews."
Liam has previously said he wouldn't like to endorse condoms - unlike their rival boy band JLS - because there would be too many jokes made at the group's expense.
But Liam didn't find it funny when he visited the Empire State Building in New York City earlier this week and took to Twitter to slam the security staff for being "extremely disrespectful" to his family.
In a series of tweets, which have now been deleted, he wrote: "Just been to the Empire State Building had a great time except...
"The security detail in particular the senior security supervisor was arrogant, unproffesional and extreamly disrespectful to my family @EmpireStateBldg #TheresAlwaysTimeForManors (sic)"
However, the singer has now apologized to the security team and the owners of the famous landmark for his comments.
He tweeted: "Seems there was a bit of a mix up when I was at the empire state. Its all good. Sorry for confusion looking fwd to next timeeeee!
"I would like to formally apologise to the Empire State Building security team and its owners for our misunderstanding the other night.
"I didn't mean to cause anyone any problems and hope that I can come back again for a visit again in the future :) (sic)"
One Direction have been in America this week after performing in front of 20,000 screaming fans at Madison Square Garden in New York City on Monday night.