Google CEO Eric Schmidt and Murdoch are among those gathered at a meeting of some of the media world's most powerful figures in Sun Valley, Idaho.
It is the 27th year of the conference, which is run by investment bank Allen & Co, which has close ties to Hollywood and the technology industry.
Twitter CEO Evan Williams (pictured) is also at the conference, sparking speculation that the event is a good opportunity for someone to broker a deal for the microblogging service.
Several commentators believe a deal for Twitter could be brokered at Sun Valley, the paper said.
In November 2008, Twitter rejected an offer of $500m from Facebook.
One of the main reasons to reject the offer was that Twitter's investors believe it has opportunities to grow and that accepting the first offer on the table would restrict its potential.
Twitter has recorded a 22-fold increase in traffic in the past year, according to Hitwise, which analyses internet usage, making it the fastest growing site in the UK.