Pompey are currently in administration and the club's creditors - owed a reported £24million - will vote on Monday whether to accept Balram Chainrai's Company Voluntary Agreement, while the Pompey Supporters Trust are still hopeful of launching a rival bid.
"If we can get three players out by the start of pre-season that will be very helpful," Appleton told BBC Solent. "Hopefully the CVA will get approved. Then there will be a period of time when Balram Chainrai takes the club over.
"In that period of time I'm not sure how many players, if any, I'll be allowed to bring into the football club. I would imagine it would be a difficult period of six weeks until the season starts.
"From a motivational point of view it's a lot easier to get your squad together at the start of July and work with them from then.
"You can get them ready, gel during pre-season, work on the dynamics of the squad, get them to play how you want. I'm not going to be lucky enough to do all those things."