Both News Corp and DMGT, which owns the Daily Mail, also fear the rules will harm their ability to leverage debt and secure investment in future.
Lobbyists are understood to have warned that the move could devalue the wider market for news publishers at a time when the Government is attempting to ensure the sustainability of newspapers.
In its consultation, the Government has proposed to increase the cap to 10pc for diversified businesses whose UK newspaper holdings account for 20pc or less of their global turnover.
This is designed to ensure that the rules do not prevent companies from raising investment from foreign states for other parts of their business.
Ministers also proposed excluding small shareholdings or retail investments made by senior figures in foreign governments and their families as they would not be expected to hold any influence.
The move to block the UAE takeover of The Telegraph, which was outlined in an amendment to the Digital Markets, Consumer and Competition Bill (DMCC), comes after MPs raised concerns about the impact of the sale on press freedom.
The publications of both Mr Murdoch and Lord Rothermere were also vocal critics of the swoop by RedBird IMI, a fund majority-backed by UAE vice president Sheikh Mansour.