Varney in talks with Leeds
Varney and Norris are heading for the Fratton Park exit as Pompey continue to slash their wage bill as they prepare for life in League One.
Former Charlton and Derby forward Varney has held discussions with Leeds and could complete his move to Neil Warnock's side in the coming days.
Midfielder Norris has also been linked with the Elland Road outfit, with Sheffield Wednesday reported to be another club interested in his services.
Appleton admitted the 31-year-old former Ipswich player was in discussions with a team from England's second tier, but did not disclose their identity.
Appleton told the Portsmouth News: "I believe Luke has been in talks with Leeds. Whether that (move) will happen this weekend or next week, we'll have to see.
"David is also in discussions with a Championship club and I will be surprised if there weren't others interested in him.
"I know they are both close to agreeing moves elsewhere."