The former England international is expected to discuss the new TV role with BBC in October.
Barker has left her role hosting the long-running sports quiz role, a position she held for 24 years.
The Sun quoted an insider: “Like Sue, she’s a former sportswoman and she also has five years of broadcasting under her belt.
“This has nothing to do with gender, nor is it a case of the BBC trying to be woke.
“While a lot can happen over the next three months, as things stand Alex is genuinely considered the best woman for the job.”
Scott has plenty of television experience since retiring from football in 2017, including punditry work for both the BBC and Sky, and has past presenting gigs with the former.
Barker told the Mail last week that he was sad to be leaving her “dream job” but understood BBC’s decision.
“I love the show so much they would have to remove me, it would have been tough for me to walk away.
“I’ve absolutely loved my 24 years fronting A Question Of Sport, it’s been my dream job,’ she said.
“But I understand the BBC want to take the show in a new direction and I’m sad to say goodbye.”