Couples who donate $50,000 earn a spot at a private dinner at a home in Shorewood.
The invitation says the fundraisers will be the "one and only event that Governor Romney will attend in Minnesota," MPR reports.
The fundraiser would fall one week before Romney accepts the GOP nomination for president at the Republican National Convention in Tampa Bay, Fla.
It also fuels speculation that Romney could pick former-Gov. Tim Pawlenty as his running-mate, MPR notes.
Romney was beaten by former Pennsylvania Sen. Rick Santorum in a nonbinding straw poll during Minnesota's February GOP caucuses, the Associated Press notes in its story.
But a recent poll shows Romney cutting into Obama's lead in the state.