Newton came under fire Wednesday for laughing at a question from Charlotte Observer writer Jourdan Rodrigue about receiver Devin Funchess and saying "it's amusing to hear a female talk about routes".
Prescott is set to shoot his first TV spot for Dannon later this week in Dallas, Schefter reports.
Dannon is working with a new National Football League quarterback after parting ways with Cam Newton.
Dannon distanced itself from Newton after he made sexist remarks toward a female Charlotte Observer reporter Jourdan Rodrigue on Wednesday.
White House: Take Trump's priorities seriously, not his comments
However, stories are still doing the rounds that Trump and Tillerson's relationship has been damaged beyond fix due to clashes over Iran and North Korea policy.
This marks the latest in a slate of sponsorships that will pay Prescott $3 million this year, dwarfing his Cowboys salary of $544,000.
That brought an immediate and mushrooming reaction on social media that ballooned into media coverage and included Dannon announcing that it would no longer use Newton as the spokesman for its Oikos Greek yogurt.
On Thursday, Newton finally apologized to what he describes as "extremely degrading and disrespectful" action, during a postgame presser following the Panthers' win over the New England Patriots last Sunday.
Newton has since apologized, saying that he tries to be a role model in the community and that the remarks were "extremely unacceptable".