The Local Authority Pension Fund Forum, or LAPFF, which represents 71 public pension funds in the U.K., warned Fox that its planned acquisition of the 61% of Sky that it doesn't already own should include a steeper premium for shareholders. It also asked for "management safeguards" in an apparent reference to the phone-hacking scandal that engulfed Murdoch-owned news operations in 2011.
"LAPFF will scrutinise the process carefully against previous company statements," said LAPFF Chairman Kieran Quinn. "To ensure public shareholders are not disadvantaged, any takeover bid would need to be put to a shareholder vote and any recommendation by the board in favour would have to be based on an appropriate premium as well as safeguards for future probity given past track records of the businesses controlled by the Murdoch family."
In addition, LAPFF said that it would welcome the involvement of U.K. regulator OFCOM if it were to decide to investigate the 'broader impact' of the deal on the broadcasting and print media market.
While the preliminary £11.2 billion ($14.3 billion) offer hasn't been formally accepted, analysts have said that a final announcement could come as soon as Wednesday.
Sky stock was up by 1.7% to 988 pence in London by 15:00 GMT Tuesday and still some 10% below the offer price of 1,075 pence per share.
Gripes among minority shareholders over the offer price are not without merit.
The 36% premium offered by Fox merely takes Sky shares back to where they were in January, before the target's stock was hit by concerns over competition and uncertainties stemming from the U.K.'s vote to leave the European Union in June.
Cost-inflation for sports broadcasting rights in the U.K. and Europe, and competition in pay-tv from BT (BT) , has also been a key issue for Sky shareholders.
BT's entry into sports broadcasting and pay-tv in recent years has forced up the price of rights for the U.K's Premier League football, leading Sky to pay 80% more (£4.2 billion) in 2015 to air the games. It also led the target to lose the rights for European UEFA Champion's League football in 2013.
But Sky shareholders are not the only ones left with a sour taste in their mouths by Fox's bid, a second attempt by Murdoch controlled entities to gain control of the broadcaster.
Moody's Investors Service Monday placed Fox's Baa1 senior unsecured debt rating -- which sits two notches above the investment grade threshold -- under review for a possible downgrade given the threat posed by the acquisition to its balance sheet.
TheStreet also reported that Fox's stretched balance sheet that might constrain the company's ability to pay dividends and carry out share buybacks.
The silver lining in all of this for critics is that two-pronged opposition to the deal, from shareholders in both camps, and the threat of a ratings downgrade might be enough to knock Murdoch off-course for a second time.
Fox stock has fallen by around 6.5% since news of the offer emerged Friday and was trading around $26.35 early Tuesday in New York. It has until Jan. 6 to make a firm offer for Sky or to walk away.