"The likelihood of it going to her is high. She's very well liked here [at the show and network]," the source told ET. Hager would potentially fill Gifford's seat in the show's fourth hour during Hoda & Kathie Lee after Gifford leaves the program on the hour's 11th anniversary, April 7, 2019.
Hager, a Today show contributor and correspondent since 2009, has appeared more and more often on the show, filling in for Hoda Kotb or Gifford in the fourth hour or often covering for Carson Daly in the Orange Room during the 7-9 a.m. block.
The 39-year-old, who is the daughter of former president George W. Bush, has also worked as a teacher and an author.
Fans have been calling for Hager to replace Gifford since Gifford, 65, made the announcement that she was leaving the show.
"The only person I want in that chair after KLG is [Jenna Bush Hager]," one fan tweeted after Gifford's announcement.
Hager has not commented on potentially filling Gifford's shoes, but did send a heartfelt message of love and respect to her co-worker.
"We adore you KLG. Thanks for your love, friendship and for your hilarity. You will be dearly missed," she tweeted.
Other fans are hoping that former Today anchor Ann Curry return to the show in Gifford's place.
Gifford announced the news in a tearful broadcast Tuesday morning, expressing her gratitude to the show's crew as well as her co-host and close friend, Kotb.
"I have something to share with everybody and it's bittersweet, as these things always are, but I've been here almost 11 years," she began. "Thought I would stay one year. Something happened along the way. Fell in love with a beautiful Egyptian goddess and now, when it's our 11th anniversary, I'm going to be leaving the Today show. It's an exciting time for me and I'm thrilled about all the projects that are coming up, but it's also hard because the reason that I stayed longer than a year is because I love everybody here so much."
Later on, she explained that she has several creative projects on her plate, including making her directorial debut with a short film in Israel. She also hinted that she "sort" has a project coming with Dolly Parton and Roma Downey as well.
"The roadblocks are gone. It just seems like it's the time," she said.
The Today show airs weekdays at 7 a.m. ET on NBC.