The Sun newspaper reported claims that the Batley-born former Coronation Street and Emmerdale actress, who was a friend of late MP Jo Cox, is expected to announce a campaign to run for the seat.
According to its report, which was published online today, sources have said the 55-year-old would be the “perfect replacement”.
She has since replied to a BBC Radio Leeds tweet saying: “I’m thinking about [it] and need to talk to the people of Batley & Spen.”
Ms Brabin campaigned alongside Mrs Cox to save Batley Library from closure when the Labour politician was a parliamentary candidate.
The Sun’s report says that Ms Brabin has the backing of the local Labour party.
But the Daily Mail previously published an article which claimed that former MP David Miliband has been urged to stand for the seat as a way to mount a Labour leadership campaign against Jeremy Corbyn.
No date has yet been set for the by-election but it is understood that it will not take place until October at the earliest.
Mrs Cox was killed on June 16 this year outside Birstall’s library.