Saint-Maximin had a starring role as Newcastle emerged from Anfield with a point on Saturday afternoon, flummoxing the Reds defence with his movement and skill during the 1-1 draw.
After the match, one Liverpool fan tweeted Saint-Maximin to ask him if he would be interested in a potential swap deal with Mane moving in the other direction.
But the Frenchman issued an emphatic response, accusing the supporter of being "ungrateful" and insisting he is "a long way" off Mane's quality.
"I know you think it's a nice message to me but I don't like this," wrote Saint-Maximin on Twitter.
"Be respectful to him please, you are ungrateful, he did and he's doing a lot for Liverpool, there is still a long way before I could reach his level."