Despite a field of candidates who regularly bash the news media and a continuing tussle with the Commission on Presidential Debates, Republican leaders sat down last week with television executives in New York and posed a question:

Do you want to host a debate?

In an intriguing show of détente, the Republican National Committee has asked several major TV networks — including CNN, a regular Republican boogeyman — to consider sponsoring debates, an early sign that the party is making plans for a contested presidential primary.

The debates would probably begin this summer, and Republicans are casting a wide net: Party officials are also in talks with executives from ABC, CBS, NBC and Fox News, along with more-niche networks like Newsmax and NewsNation, according to several people who requested anonymity to describe discussions intended to be private. Political debates are highly prized in the TV news industry, and the networks are expected to present proposals next month.

“Our goal is to have incredibly successful debates that allow Republican primary voters to see, without any kind of bias, a full picture of what these candidates stand for,” David Bossie, the chairman of the party’s presidential debates committee, said in an interview.

The conversations, led by Mr. Bossie and Ronna McDaniel, the R.N.C. chairwoman, have moved forward even as the Republicans’ slate of presidential contenders remains uncertain. They underscore a delicate balancing act for Republican leaders, who are reviewing media and messaging strategy after a poor showing in last year’s midterm races.

Several Republican candidates in 2022 who spoke only with conservative outlets and podcasters were defeated in November — losses that raised questions about the power of partisan media to reach the swing voters who often determine the outcome of tight races.

But other leading Republicans found success in ignoring the mainstream press. Gov. Ron DeSantis of Florida, who is viewed as a likely 2024 presidential contender, easily won re-election without submitting to interviews with nonpartisan outlets or local editorial pages. Former President Donald J. Trump, the only Republican who has declared his intention to run in 2024, continues to assail journalists.

In the interview, Mr. Bossie acknowledged that Republicans remained “incredibly skeptical that our presidential candidates can get a fair shake from what we consider the biased mainstream media.” But he said Republican leaders could still engage with national media outlets that conservative stars routinely criticize.

“There are plenty of Republicans who consume their news just from the major networks,” Mr. Bossie said. “That’s why we have a broader outreach.”

Mr. Bossie said he would “demand fair and unbiased moderators and questioners,” adding: “We are fighting for that fairness. Our goal is to have a debate without anybody even remembering who a moderator is, or if there was a moderator.”

The R.N.C. is unlikely to turn to MSNBC to sponsor a primary debate, partly because the network’s left-leaning audience has little overlap with the primary electorate, according to a person with knowledge of the party’s plans. But the early talks have included NBC properties like CNBC, Telemundo and the NBC broadcast network.

There is precedent for political parties bypassing specific networks. In 2019, Democratic officials refused to grant one of their primary debates to Fox News.

“We cast a broad net to engage with interested and qualified organizations, though not every entity who submits a proposal will receive a debate,” Ms. McDaniel said in a statement.

Aired to mass audiences by broadcast and cable networks, debates are a tradition that often produce pivotal moments in campaigns. For long-shot candidates, they can be hugely beneficial (Mr. Trump’s fiery exchange in 2015 with Megyn Kelly, a Fox News anchor at the time) or hugely destructive (Senator Elizabeth Warren’s dismantling of former Mayor Michael R. Bloomberg of New York in 2020, effectively ending his presidential candidacy onstage).

Networks typically foot the significant costs for holding a debate, including paying for the venue rental and production crew; in return, TV executives secure big ratings and big revenue. Primary debates in 2015 and 2019 broke viewership records. In the 2016 race, when both parties’ nominations were openly contested, CNN hosted more than a dozen primary debates and candidate forums; the network often made up to $2 million in profit from individual events, according to a person with knowledge of internal financial figures.

The electoral matchups also place news networks at the heart of the national conversation and highlight their civic role. Cable channels often choreograph days of Super Bowl-like coverage around a primary debate, complete with onscreen clocks counting down to the main event.

Recently, however, debates have faced an uncertain future.

The Republican Party last year formally boycotted the Commission on Presidential Debates, the nonpartisan group that has sponsored every general election debate since 1988, deeming it “biased.” The R.N.C. has not backed away from that stance. (Primary debates are organized directly between political parties and media organizations, without the participation of the independent commission.) In the 2022 midterm elections, some high-profile Republican and Democratic candidates declined to appear on a debate stage with their opponents.

Even if Republican officials wrap up plans for a primary debate with a mainstream network, it is not clear if candidates who attack the news media, like Mr. Trump or Mr. DeSantis, will participate.

In 2020, Mr. Trump pulled out of the second of three scheduled general-election debates after the commission decided to hold the debate virtually because of concerns about the coronavirus; the event was canceled.

In 2016, Mr. Trump withdrew from a Fox News debate on the eve of the Iowa caucuses after the network rejected his request that Ms. Kelly be removed as a moderator. Two months later, when Mr. Trump announced that he would skip another Fox News debate in Utah, the network canceled the event.