Two top 10 shareholders in BSkyB
The Sunday Telegraph said Legal and General (L&G) will vote against Murdoch, while the Sunday Times said Kames Capital has urged Murdoch to quit. A third big investor, the Local Authority Pension Fund Forum (LAPFF) is also set to vote against Murdoch's re-election.
Kames Capital and L&G were not immediately available for comment.
The Sunday Telegraph said while L&G raised no ethical issues about the way Murdoch operated, its concerns related to his ability to retain independence following News Corp's
The Sunday Times also said Kames Capital will vote against his re-election as it wants an independent chairman.
L&G has a 2.9 percent stake in BSkyB, while Kames Capital has 1.6 percent, according to Reuters data.
LAPFF, which owns around 1 percent in BSkyB, said in a statement on its web site it had conducted extensive research into the phone hacking scandal at News Corp and had also engaged with BSkyB, leading it to believe that the company would now benefit from an independent chair.
Earlier this month, the company's independent directors unanimously backed James Murdoch as chairman in a letter addressing shareholders' concerns about his suitability following the phone-hacking scandal at the News of the World.
(Reporting by Adveith Nair and Michelle Martin; Editing by David Holmes)