Toffees full-back Jonjoe Kenny won promotion with the O's last season.
Appleton wants Kenny back
Kenny joined the O's on a temporary basis in January and helped them to promotion as League Two runners-up.
With his mission complete, the right-back returned to feature in Everton's final Premier League game of the campaign against Norwich City and was heavily involved in the goal scored by Kevin Mirallas.
Kenny made his Premier League debut last month
His performance is unlikely to have done Appleton any favours, though the former Manchester United midfielder has not given up hope of a reunion with Kenny.
Asked if he would want the 19-year-old back, Appleton told the Oxford Mail: "There’s no doubt about that, he did well here.
Kenny recently helped Oxford into League One
"Everton think very highly of him. As it stands I get the impression they want him back for pre-season, which I completely understand.
"Whether (signing him) is an option at the start, middle or back end of pre-season, we don’t call the shots on that one.
"Everton are the ones in control and they may even see him being very close around their first team."
Kenny's first team chances are set to improve this summer, with long-serving right-back Tony Hibbert out of contract at Goodison Park.
And, if his track record is anything to go by, imminent Everton appointment Ronald Koeman is unlikely to hesitate about promoting the England Under-19 international.
Kenny celebrates winning the European Under-17 Championship with England
Koeman's arrival from Southampton, where the Dutchman has handed debuts to Matt Targett, Jake Hesketh and Ryan Seager among others, is set to be confirmed this week.