McDermott, appointed in April last year after being sacked by Reading, was reportedly fired on Friday.
The club's owners - GFH Capital - put out a statement on Saturday saying McDermott was still in charge, although he was not in the dugout when Leeds crushed Huddersfield Town 5-1 in front over 31,000 fans, many of whom showed their support for the 52-year-old.
GFH has agreed to sell 75 percent of the club to Eleonora Sport Limited which is owned by the Cellino family who also own Italian Serie A side Cagliari.
McDermott returned to the club's training ground on Monday, but later told a news conference that while he was still in charge, there was no guarantee about his future.
"I've no idea if I'm more secure now," he said.
"I can't answer that. The most important thing in football is to win games.
"When I came in I signed a three-year deal and we talked about a long-term vision with a direction for the football club with stability."
McDermott said it would have been easy to walk away from the club, currently 11th in England's second-tier, but he had no intention of resigning.
"Some big people in the game have said don't go back. But how can I not go back? There is no way I would leave the group of staff I have here and the supporters. My job now is to get results. The bigger picture is the stability of this club moving forward and that's what I was put in this position for.
"Not too many people have said stick with it. For me, walking away would have been the easy thing to do. I wasn't interested in that, I want to be Leeds United manager."
McDermott said he was responsibly for all "football matters" at the club, and no-one would be allowed into the dugout or dressing room without his permission.
The sale of the club is subject to Football League approval, and McDermott said it was important the ownership situation was resolved as quickly as possible.
Leeds, English champions in 1992, have failed to regain their top-flight status following relegation from the Premier League in 2004. (Reporting By Josh Reich)
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