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Sky's independent directors are under mounting pressure to secure a higher bid from Rupert Murdoch for the 61% stake in the satellite broadcaster it does not own.

On Friday, 21st Century Fox announced a possible bid for Sky priced at £10.75 a share, valuing the company at £18.5bn.

Investors are concerned that James Murdoch is both chairman of Sky and chief executive of Fox.

The deputy chairman is Martin Gilbert, Aberdeen Asset Management boss.

He is also the senior independent director.

Thomas Moore, investment director at Standard Life Investments, said the deal would be a "real test" of the non-executive directors.

The presence of James Murdoch on both the Sky and Fox boards meant "this can't be an arms-length deal", he told the ´óÏó´«Ã½.

"There's heavy representation of people aligned with Rupert Murdoch, not just James Murdoch," Mr Moore said.

"We hope that Martin Gilbert will step up and put forward a strong case that this bid undervalues the company."

Other non-executive directors on the include Chase Carey, a former chief executive of Fox Television and co-chief operating officer of News Corporation. That company owns Rupert Murdoch's newspapers, including the Sun, the Times and the Wall Street Journal.

Another non-executive director, John Nallen, is chief financial officer of 21st Century Fox.

Fox said on Friday that Sky's directors had indicated that they were willing to recommend the proposed offer.

Standard Life has a 0.26% stake in Sky, with just under 4.4 million shares.

"Shareholders - our clients ultimately - are reliant on this independent board to come up with a solution which will represent proper value," Mr Moore said.

"There are concerns, given the composition of the board, that that cannot be the case. We would hope this is a starting bid and on reflection they will appreciate that a higher bid is more appropriate."

Shares closed on Friday just under £10, suggesting some investors fear the deal may not go through. The stock was trading at the same level as the offer price as recently as April, but fell sharply in the wake of the Brexit vote.

Sky fell a further 1.4% in early trading on Monday to 986.5p.

Alastair Gunn, a fund manager at Jupiter Asset Management, said this weekend that the Fox approach "ought to be the start of the process, not the conclusion".

Another Sky shareholder : "Our initial reaction is one of serious disappointment that they have rolled over like this."

Piers Hillier, chief investment officer of Royal London Asset Management, told the Times that Mr Gilbert should replace James Murdoch as chairman.

"He [James Murdoch] should never have been made chairman in the first place," Mr Hillier said.

BlackRock, the second-largest shareholder in the broadcaster with a 5.49% stake, declined to comment on the Fox bid.