Talks are ongoing between Tullett Prebon chief Terry Smith and GFI Group Micky Gooch, owners of the UK's second and third-largest IDBs respectively, to merge the two firms.
This would bring the new broker into direct competition with Michael Spencer, who runs industry-leading Icap.
IDBs are a very profitable, but secretive, sector in the financial services industry.
They work by providing links between traders who want to conduct equities, property or debt trades anonymously - and therefore allow big sums to be transferred without rival firms being alerted.
The putative conflict has already been dubbed "class war in the City" by the newspaper - which pointed out the contrasting personalities and backgrounds of the two IDB bosses.
While Mr Smith enjoys watching greyhound racing, Mr Spencer prefers to watch international rugby being played at Twickenham - seen as a traditionally middle-class pursuit in the UK.
Speaking to the newspaper, the Tullett Prebon head added: "[I'm] as unpolitically correct as you can get. I'm probably the only chief executive who goes to watch boxing in [working-class east London district] Bethnal Green."
"Talks [with Mr Gooch] are going very well and have been very constructiveâ¦there's always a danger of Mr Spencer intervening in one way or another because he recognises that we will be such a strong competitor to his business."