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[Harry Potter] Does Snape know who's Cursing Harry's broom? Spoliers for the 1st book

During the Quidditch match Quirrell is cursing Harry's broom and even says he would have succeeded even with Snape preforming a counter curse

so did Snape know Quirrell was the one cursing it?
gpt
Edit: The Gryffindor vs. Slytherin match occurred in November. By Quirrell's account, Snape already knew who he was by at least Halloween.

~~I don't recall if Quirrell states exactly when Snape discovered him, but he clearly does early on. So, it is reasonable to assume that he did know Quirrell was behind it.~~