Two companies are believed to have contacted Twitter with "serious" interest, with Google identified as one of those firms, media reports said.
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The micro-blogging site has reportedly hired Goldman Sachs as an adviser to spurn the advances. Ten-year-old Twitter has a market capitalisation of more than $34 billion with 288 million monthly active users.
Google has a $60 billion cash pile and according to analysts, it has struggled so far in the social media arena against Facebook.
Like Microsoft was threatened by Google, Google is threatened by Facebook which is doing a better job than any other internet company of competing with Google for user attention and ad revenues.
Rumours that Google is interested in buying Twitter are in the circulation for years and reports suggested that executives of both companies had held talks in 2011, Telegraph reported.