Hart is still favourite to take over from Eddie Gray at Elland Road, despite joining Barnsley last week.
"It is understandable that my name would be linked with Leeds United because I spent 10 years of my working life there. But that's all I know," he told the Yorkshire Post.
"The rest is rumour mill and speculation."
Asked if he had considered keeping his options open, Hart added: "Not really, because I am not an arrogant man and I don't think I can just click my fingers and get a job.
"I have not considered what might happen further down the line. I am just here to do a job and do what I always do which is try and build."