Kenny, 34, joined the Championship side during the summer after it is understood he asked for a transfer, despite the Hoops hoping he would stay to provide competition for summer signing Rob Green.
The England international endured a nightmare debut following his move from West Ham, with a blunder for the first goal putting Swansea on course to a 5-0 victory in the season's opener.
It is understood Kenny sent abusive text messages to R's technical director Mike Rigg and Fernandes late on Saturday night and in the early hours of Sunday morning, mocking the result and Green's performance.
Rigg is also understood to have received calls up until 3am on Sunday, leading him to make a formal complaint to Leeds.
The accusations are likely to further damage Kenny's status at QPR, who he described as a "tin pot club" on Twitter in recent days.
Leeds manager Neil Warnock refused to comment on the matter at Thursday morning's press conference previewing Saturday's Championship trip to Peterborough other than to confirm it is being dealt with internally.
"We have a club policy on Twitter and social networking. It's an internal matter and we will not be commenting further," he said.
