Discussions with the search engine giant and social network are said to be “low level”, according to the Wall Street Journal.
The valuation of $8bn to $10bn is more than double the $3.9bn price tag reported a year ago.
It is not known if a formal offer has been made but Twitter’s management has previously said it would remain a privately owned venture.
Twitter is estimated to have reported revenue of $45m last year and is expected to make between $100m to $110m in 2011.
Last December it raised $200m from investors including venture capital firm Kleiner Perkins Caufield & Byers and existing Twitter investors which pushed up it value.