Barry, a league winner during his time with Manchester City, will overtake Giggs' all-time record of 632 games if he features in all 38 fixtures next term.
"You've got to keep that desire and make sure you are driving into training every day wanting to give 100 percent," Barry told the club's website (www.evertonfc.com).
"I want to keep going because there is plenty of time after football to relax. Whilst you can still play football, why not keep doing it?".
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Everton finished 11th in the league this season.
(Reporting by Nivedita Shankar in Bengaluru; Editing by Tony Jimenez)
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