Pompey's relegation was confirmed last weekend and the future remains uncertain with the club still in administration, desperate to slash the wage bill further and unable to offer contracts to players.
"Everyone is looking for free transfers at this time of year," boss Appleton told the club website. "It's slightly frustrating because if, for instance, someone is out of contract at another club, I can't physically offer them a contract here.
"So what I have to do when I speak to people is to make it really personal.
"I'm sure I'll be spending a lot of time in my car over the next few weeks going up and down the country, meeting players and agents and making it very, very personal, because that's the only way I'm going to get players on board to come and play for Portsmouth.
"We're going to be one of the big fish in League One next year. I'm sure we'll have fantastic support again, and hopefully that will be enough to encourage players to hang on for us."
