Found something - a Johns Hopkins Bloomberg School of Public Health - a paper that reads like a talking points memo for gun control - the paper references:
"Data from a nationally representative sample of gun owners indicate that 40 percent of firearm acquisitions are from individuals who are not licensed gun dealers."
While the rest of the paper seemingly has footnotes for most references, there is no reference for this statistic, just the statement itself.
However, there is no way to even theoretically regulate private sales without registration of all guns. So they get two birds with one stone.
Of course rarely say - "We want to ban all private sales and register all guns." that would lose support so they say "We must close the loophole that allows 40 percent of all guns to be sold without a background check."
Still wonder about the documentation for that 40 percent figure - what those sales include - who did the survey - how was the survey conducted - how were gun owners chosen - how many were surveyed - where is the methodology and raw data available?