Mellon was unexpectedly sacked on Saturday evening following the Cod Army's FA Cup exit at the hands of Aldershot, their third successive defeat in all competitions, although they remain seventh in League Two.
Formerly Mellon's number two, Madden is preparing the squad for Saturday's home game with Southend and, despite encouraging words from chairman Andy Pilley, he is accepting no assurances over his future.
"The chairman has said he doesn't want me to go and is happy with the backroom staff, but we'll have to see what happens," he told the Blackpool Gazette. "A new manager may very well want to bring in his own number two.
"We had a meeting with the chairman on Monday and he told us that people have applied already.
"He told us there is no timeframe. He will sift through the applications and will take his time. He said he would keep us up to speed. I wasn't tempted. Being a manager isn't me and I'm happy to concentrate on the coaching side.
"It was made clear at the meeting that somebody new is going to come in and I honestly hadn't thought about going for it myself."
Madden revealed Mellon's departure had unsettled members of the playing staff.
He added: "I think it came as a shock to everyone. The lads were very flat, which wasn't a surprise because some of them had worked with Micky since the Blue Square North days. Some of the lads who have played at a higher level have seen all this before but it's never nice."