Cash-strapped Pompey have been set a August 10 deadline by administrators to have their finances in order or face going out of business.
Appleton revealed he has stepped in to end stand-offs between players and the administrators.
"I have spoken to numerous players over the last few days regarding everything that is going on," he told the Portsmouth News. "There is a bit of slow progress, so hopefully come the end of the week there might be a bit more light at the end of the tunnel in terms of people leaving.
"I have been worried about the situation and it is something I felt I had to do. I wanted to reassure these players and keep them as up-to-date as much as I possibly can. Possibly, a different voice will help. That is why I tried to intervene a little bit and help the situation.
"It seemed to work because two have gone [Luke Varney and David Norris] and I think another [Erik Huseklepp] is just around the corner."
