Chief operating officer Chase Carey said he would be open to discussions over a sale or partnership, with web giants Yahoo and AOL linked to a deal.
It is not clear how much News Corp would expect to receive for the site but it would be a fraction of the $580m that it paid for it five years ago.
Carey said: “There are opportunities here to do 20 things but that doesn’t mean you’re going to do any of the 20. If there’s something there that makes sense you ought to think about it.”
The admission is a stark change of tack for News Corp, which has repeatedly denied suggestions it is trying to offload the social network.
MySpace has fallen from being one of the internet’s fastest growing sites to an embarrassing weight around Rupert Murdoch’s neck in just five years. It has suffered from intense competition from Facebook, which now has more than 500m users, and Twitter.
Last month Facebook had 151m unique users, compared to just 60m at MySpace.
Analysts have been speculating for years that it will end up going the same way as Bebo – also a once promising social network – which AOL has sold for a fraction of the $850m it paid in 2008.
MySpace has also lost several top executives including co-president Jason Hirschhorn in June. Hirschhorn, with fellow co-president Mike Jones, replaced former chief executive Owen Van Natta just four months earlier.