Ms Phillips already sparked speculation that she plans to run for the top job when she tweeted a graphic on Tuesday which says, “2020” and “Watch this space”.
The backbencher is likely to announce her formal bid this evening as reporters wait on standby for the announcement, the broadcaster reported.
It comes as she branded a US airstrike against Iran early on Friday morning as “reckless foreign policy”.
The country’s most powerful military commander General Qasem Soleimani was killed during the attack ordered by President Donald Trump.
Presenter Nick Robinson commented on the Labour MP’s reaction, saying: “It matters because it looks as though she may become the latest candidate who wants to replace Jeremy Corbyn as leader of the Labour Party.”
Ms Phillips’ office has been contacted by the Standard for comment.
Former Labour MP for Great Grimsby Melanie Onn said Ms Phillips would be in a “very good position to be able to reach out to ordinary people” if she were to formally stand for the Labour leadership.
Ms Onn, who lost her seat in the December election, told the programme: “Well, we haven’t had everybody declaring who is going to stand as yet, but I’m really looking for somebody who is going to be honest.
“I’m looking for somebody with a USP that is going to transcend normal politics, I’m looking for somebody who is going to be unafraid to share their views and opinions and be prepared to back those up with very strong committed arguments,” she added.
“And I think that at the moment, while we’ve got Boris Johnson as Prime Minister, we need somebody with an incredibly strong personality who’s not going to be afraid to stand up to him and is going to scrutinise him in a way that he does not appreciate.”
Ms Phillips, who leans on the soft left of the party, has been an outspoken critic of Jeremy Corbyn’s leadership as well as speaking out against the war in Iraq during Tony Blair’s tenure.
Her candidacy would offer one of the cleanest break from the politics of the Corbyn era.
Since the party’s disastrous defeat at the December 12 poll, Ms Phillips has been campaigning for people to join Labour in order to change it.
Despite many Labour leave seats falling to the Tories, there was only a small swing in her constituency while she was a Remainer standing in a Leave area.
Sir Keir Starmer is current favourite to succeed Mr Corbyn, according to a poll .