Gallagher is close to signing a long-term deal to title sponsor Premiership Rugby, according to UK media reports.
The Chicago-based insurance broker is set to replace current sponsor Aviva, which has sponsored England’s top-tier rugby union club competition since 2010.
The Guardian says that the move could involve a regular league fixture being played in Chicago.
Aviva, the UK-headquartered insurance company, had been paying around US$7 million per year for the naming rights to the Premiership.
It is hoped the new deal, which is understood to be worth several millions of pounds, will help strengthen the sport’s profile in the US. The league has staged several regular-season matches in the country in recent years.
Gallagher is also an official insurance broker of Premiership outfit Wasps.
"Premiership Rugby is at an advanced stage of confirming our title partner for the start of the 2018-19 season," a spokesman told the BBC. "We can't comment on the names of any companies who are part of this process."