The phrase "almost no connection" is correct and usable in written English.
It can be used to describe a situation where there is very little or negligible relationship or link between two things.
Example: "After reviewing the evidence, it became clear that there was almost no connection between the two incidents."
Alternatives: "barely any connection" or "little to no connection".
She lodged a criminal complaint in a country with almost no connection to the book or the review.
There was almost no connection between the American movies-and-music division and the Japanese electronics division.
Old-growth forest was less fragmented, but was concentrated mainly in two large regions (the Andes and Coastal mountain range) with almost no connection in between.
Let the Dow rise, let the Dow fall; a death payout is an uncorrelated asset whose timing bears almost no connection to the mood swings of the market.
Undoubtedly, "Thrift Shop," which also features the singer Wanz, is a hip-hop song, though one that bears almost no connection to hip-hop as a living genre.
Judge Nelms used those pages to rail against the practice of large corporations filing bankruptcy cases "in venues that have almost no connection to the debtor".
Cuvier had grown up in a small town on the Swiss border and had almost no connections in the capital.
Relatively immature kerogen (whose actual age depends of the combination of temperatures and pressures it has been subjected to) tends to have much larger pores but almost no connections among those pores, making it much harder to extract the fuel.
A memorable network graphic of the war's Twittersphere showed almost no connections between the "blue" internet – of Israelis, the Jewish diaspora and the US Tea party – and the "green", which included the Muslim world and the anti-war movements in the west.
Choreographically, "Flowers" had almost no literal connection to botany.
William Golding's wild and visionary Darkness Visible (1979) - Milton was very much in the air in the late 70s - makes almost no rational connection between the poles of its plot, the amoral twins Sophy and Toni, possessed of "phenomenal intelligence" and a destructive urge, the mystical outcast Mattie and the paedophile schoolmaster Sebastian Pedigree.
