Taylor, 23, is out of contract in the summer and head coach Garry Monk revealed after his side’s 1-1 draw at the DW Stadium in the final league game of the season that the defender had made himself unavailable to travel.
Monk said Taylor was “naive” and had been “ill-advised” in his post-match press conference, adding his behaviour had been “unacceptable” and that the club would take a strong stance against it.
Leeds refused to comment when approached by Press Association Sport, but it is understood the disciplinary process is under way.
Taylor, who progressed through the club’s academy after joining as a nine-year-old, had a transfer request turned down last summer after being linked with Premier League clubs West Brom, Middlesbrough and Crystal Palace.
He refused to enter into talks over a new contract - he signed a three-year deal in June 2014 - and it has been widely reported that he will join West Brom when his current deal expires.
Leeds will be entitled to compensation for the player, expected to be a seven-figure fee, as he is under the age of 24.
Taylor made his league debut for Leeds 10 days before his 18th birthday in September 2011 and has made a total of 104 appearances - 32 this season - scoring three goals.