I don't know about a source, but Conway had been compiling knot tables since high school, and as a knot with only 11 crossings, the Conway knot is certain to ha

I don't know about a source, but Conway had been compiling knot tables since high school, and as a knot with only 11 crossings, the Conway knot is certain to have been on his radar. It's just such a simple knot, and sliceness such a fundamental property that Conway is sure to have tried to figure it out.