James Murdoch is poised to defend his position as Sky's chairman at its annual shareholder meeting on Thursday.
A trio of advisory firms have called on shareholders to rebel against Mr Murdoch, who is chief executive of 21st Century Fox and sits on its board.
One investor, Royal London, which owns £44m in Sky shares, has criticised the dual position as "inappropriate", amid Fox's attempted bid to take over Sky.
A Sky spokeswoman said Mr Murdoch was "uniquely well-placed" to be chairman.
The spokeswoman cited his "deep knowledge of the global media industry", adding: "It would be inappropriate for us to discuss these matters before all of our shareholders have voted."
Royal London, which has a 0.28% stake in Sky, resurfaced its concerns over the Fox-Sky deal ahead of the vote - saying the board's chairman should have no affiliation to either company.
"Minority shareholders at Sky would be better served by a truly independent chairman," said Ashley Hamilton Claxton, the firm's corporate governance manager.
"Independent oversight of the board is particularly important given Fox's ongoing bid to acquire Sky."
Mr Claxton also said remuneration arrangements could lead to "unacceptably high" levels of executive pay.
"The calculations for awarding variable pay to directors are unnecessarily complex, with multiple incentive schemes," he said.
It follows reports in the Financial Times that three advisory groups - Institutional Shareholder Services, Glass Lewis and Pirc - are urging shareholders to vote against Mr Murdoch's re-election and executive pay.
Sky's spokeswoman said: "We have one of the lowest levels of fixed pay in the FTSE 100 and shareholders have continuously voted in favour of the policy since 2014."
More than 28% of shareholders voted against Mr Murdoch's comeback as chairman last year, four years after he stood down from the position in the wake of the phone-hacking scandal at the News of the World.
Fox's bid to buy the 61% stake in Sky which it does not already own is now the subject of a Competition and Markets Authority investigation.
Telecoms regulator Ofcom earlier said the deal risked giving the Murdoch family "increased influence" over the UK's news agenda and political process.
Sky is also set to update the market with results for the three months to 30 September on Thursday.