Murray instead is claiming he intends to help guide the club back to the top-flight.
"I've never been more committed to Sunderland and I'm determined to try to get the club back in to The Premiership," he told the club's official website.
"That's all I am focusing on and I feel I owe it to the fans.
"It would be easy to walk away when things are tough but I will not do that.
"If, in the future, someone wants to come in for the right reasons, with significant funds to invest in the team only, then I would do what was in the best interests of Sunderland. That is my duty.
"I would like to stress that the club has not been approached by an outside party and is not expecting to be."