The 24-year-old labelled the Leeds supporter a "muppet".
Cooper's team-mate Stuart Dallas posted a picture of himself with Rory McIlroy, before the defender asked the Northern Irish midfielder to pick up a few golf tips on his behalf.
But the Leeds fan interjected and told the 24-year-old that he would be better off asking how to "stop average Championship strikers" from getting the better of him on the pitch in a jibe which did not seem to go down well with the centre-back.
Ask him how I stop a wild FADEEEE https://t.co/l37ZZFiKKD— Liam Cooper (@LiamCooper__) May 23, 2016
Leeds fans, for the most part, will be satisfied with the Whites' season, given that relegation looked a possibility at one stage, but manager Steve Evans, who replaced Uwe Rosler in October, comfortably achieved his remit of steering the club away from danger as United finished 13th, 19 points clear of the bottom three.
That being said, it would appear as if Evans still might become the sixth manager to be sacked by Massimo Cellino, with speculation rife that he will be replaced by Darrell Clarke (Yorkshire Evening Post).