Reports suggest that the Blades made the aforementioned bid for the 19-year old midfielder on Thursday which the Buddies quickly rejected.
A source close to the Paisley club said: "The board will not stand in any player's way if the price is right but in this case, it was nowhere near right.
"The word they are using is derisory.
"The club wants to keep all its good players but knows there comes a time when they have to move on. But that will only happen if the receive fair value."
McGinn, who is the younger brother of United midfielder Stephen, has played 65 times for St Mirren since making his debut in 2012.
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