NEW YORK — A hedge fund-backed bid to buy Gannett Co., the publisher of USA Today and several other major dailies, is renewing fears of consolidation and job losses — as well as a decline in the quantity and quality of news coverage — in the already battered newspaper industry. MNG Enterprises, better known as Digital First Media, offered $1.36 billion on Monday for Gannett, saying in a letter that it can run the company more profitably via tight cost controls and consolidation of operations such as printing and administration. Gannett said its board will review the proposal. Investors gave the deal a vote of confidence, immediately pushing Gannett stock up more than 20 percent to almost $12, the amount Digital First is offering. The proposed deal is the latest indication newspapers aren’t done suffering from the punishing effects of the internet.