Julián Castro, the former housing secretary, goes on Fox News next week. Pete Buttigieg, the South Bend, Ind., mayor, earned a standing ovation (and a presidential put-down) for his Fox News town hall last month. And candidates with dismal poll numbers are taking steps to woo the network’s bookers, viewing Fox News appearances — which tend to rate higher than town halls on rivals CNN and MSNBC — as an efficient and buzz-making path to raise their profiles.

Aides to Mayor Bill de Blasio of New York City, who scorched the Murdochs last year for “creating hatred and negativity and changing our political landscape for the worse,” recently approached the network. “We want to talk to all voters about why the mayor is the best candidate for working people — regardless of what news channel they watch,” a de Blasio spokeswoman, Olivia Lapeyrolerie, said on Sunday.

Mr. de Blasio’s change of heart could be about his newly announced presidential ambitions. But it also speaks to the improbable way that Fox News — a network whose prime-time hours are often devoted to praising the president and skewering prominent Democrats — has squirreled itself into the heart of the Democratic primary.