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Kelly's public profile has increased substantially during the 2016 presidential election, in which she has been seen as tougher on Republican candidate Donald Trump than some of her Fox News peers.
The Journal reported that sources say in talks over a potential new contract with Fox News, Kelly is asking for "north of $20 million" a year, which would put her on level with Bill O'Reilly, the current ratings leader at the cable-news channel. Kelly is second in ratings at the channel.
Kelly is set to make $15 million at the end of her current contract, which expires next year.
Rupert Murdoch, Fox News' chief executive, has made it clear he would like to keep Kelly, but "it's up to her." He says money isn't an issue, according to the Journal.
Speculation has swirled over whether Kelly might jump ship, possibly to CNN or even morning or afternoon television. She's set to be a guest cohost with Kelly Ripa on ABC's daytime talk show "Live with Kelly" the day after the election.