The Sunday Telegraph reports Yahoo!'s reported interest and claims it is willing to pay up to $1bn.
Bebo was founded by British-born Michael Birch and his American wife Xochi in 2005, and is backed by private equity firm Benchmark Capital. Birch has previously said he would prefer to float Bebo than sell it.
In the UK, Bebo has overtaken MySpace to become the most popular social networking site, but globally it has around 25m users compared to MySpace's 100m.
News Corp paid $580m for MySpace in 2005, but the price of internet assets has since rocketed.
Bebo is believed to have turned down offers from BT and Viacom last year, while last year Yahoo! was in negotiations to acquire another social networking site, Facebook, for up to $1bn. However, this deal never materialised.
Earlier this month Bebo hired Angel Gambino, formerly MTV's vice-president of commercial, strategy and digital, as vice-president of music. In March it hired Joanna Shields, formerly managing direector of strategic partnerships at Google EMEA, as president, international, to expand its global presence.
In April it signed a deal to host 'KateModern' a UK-based spin-off from faux video blog Lonelygirl15, which was an internet phenomenon last summer before being revealed as a scripted drama with an actress playing the part of 'Lonelygirl15' Bree.
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