The outspoken 67-year-old, who was the MP for Bradford West between 2012 and 2015, said he may “put my own hat in the ring”.
He also criticised Labour’s selection process, after NHS worker Simon Lightwood was chosen to run in the election, and claimed local candidates had been “pushed off” the shortlist.
It comes after the entire executive committee of Wakefield’s local Labour group resigned in protest, claiming the party’s National Executive Committee intervened and decided to leave several promising local candidates, including Wakefield Council deputy leader Jack Hemingway, off the shortlist.
In a video posted online, Mr Galloway said “the best situation by far” would be for “a local candidate to emerge from within their ranks to challenge the fake Labour candidate” and if that does not happen, someone “with a track record of bridging all kinds of divisions” should stand as an independent.
He added: “The third best outcome is one that I will not rule out and that is: I pack my bags, head back to West Yorkshire and put my own hat in the ring.
“One way or another, Keir Starmer has to be defeated. Keir Starmer must go.”
A by-election will be held in Wakefield as Tory Imran Ahmad Khan resigned earlier this month, after he was found guilty of sexually assaulting a 15-year-old boy in January 2018, but no date has been set yet.
Labour had held Wakefield for 89 years, until it became one of the so-called ‘Red Wall’ seats to fall in the 2019 General Election.
Mr Galloway, who was expelled from Labour in 2003, stood in last year’s Batley and Spen by-election as a candidate for his Workers Party of Britain, but finished third.
When Labour's Kim Leadbeater won, with a narrow majority of just 323 votes, he threatened to take legal action and challenge the result in the courts.
Last month, he also threatened to take legal action against Twitter after the social media giant described him as "Russian affiliated media”.
Each of Mr Galloway’s tweets are now branded with that label, but he insisted he works "for no Russian media".
He has presented Sputnik: Orbiting the world with George Galloway with his wife Gayatri on the Russian network RT since 2013.
It comes after Ofcom revoked the broadcaster’s licence to operate in the UK following the invasion of Ukraine, stating: “RT is funded by the Russian state, which has recently invaded a neighbouring sovereign country”.