A hedge-fund-backed media group known for buying up struggling local papers and cutting costs is planning to make an offer for USA Today publisher Gannett Co., according to people familiar with the matter.

MNG Enterprises Inc., one of the largest newspaper chains in the country, has quietly built a 7.5% position in Gannett’s stock and plans to publicly urge the McLean, Va., publisher to put itself up for sale, the people said.

MNG,...