The ex-Labour and Respect MP is determined to make a return to Westminster politics and believes he can win the seat from the SNP.
Mr Galloway is reported to be keen on standing for the seat should a by-election be called.
Natalie McGarry resigned the SNP whip following allegations of fraud carried out during her time with campaign group Women for Independence.
She has since been charged by Police Scotland.
It is understood the Dundee-born politician will stand as an independent candidate opposed to a second Scottish independence referendum.
The former MP stood for the position of Mayor of London in 2016 and lost his Bradford seat in the May general election.