There's not a single verse of Scripture that states that.
And being saved, does not mean automatically free from sin.
You can be saved and still sin. It's part of being human.
So since, Mary could (allegedly) be conceived sinless in the womb of a sinful mother and (allegedly) remain sinless for the rest of her life, although still in contact with her sinful mother for the entire 9 months of gestation, then why couldn't it have happened for Jesus being born of a sinful mother.
The same way God protected Mary would have worked to protect Jesus, if indeed the sin nature is absorbed by contact or osmosis.
But it's not. It comes from the father.
So there is no requirement for Mary to be sinless in order to carry Jesus.
And here's what I want to know: do you hold that God could just as easily have allowed Mary to be conceived in original sin, and still preserved Jesus from becoming contaminated by the corruption of her sinful nature? So that when He took up His human nature, His flesh and blood and DNA and all the rest, from her, He in is human nature was still preserved from all stain of sin?
I think that's a respectable belief, by the way. I just don't know if it's your belief.