He would be very naive to leave the club right now.
When Rooney left in 2004, we had just finished 17th in the league, Radzinski had binned us off for Fulham, there was a boardroom war between Paul Gregg and Kenwright. I remember when we beat Palace away in August 2004, it was being billed as a relegation 6 pointer. Everton were a team that was going nowhere fast (or thats how it seemed to most people when Rooney left). In the end Rooney left for what was as the time, a very large sum of money.
Contrast that with Barkley's situation. We are a team knocking on the door of the top 4, with a group of young players who are improving every match. The club have shown ambition by sacking Martinez and tempting Koeman in from Southampton. Now we have decent backing from Moshiri, we are at least in a position to compete. The Everton of old would not have been in a position to sign Schneiderlin in January. Something has changed. I am confident that if he stays with the club, other good players will join in the summer and we will continue our upwards trajectory.
And he would be leaving for what? Spurs?
Good luck to them playing at Wembley next season, their record there so far has been beyond shocking. He won't be "one of there own", he will be arriving for a hefty price tag and the moment he does anything wrong the fans will turn. Spurs aren't very loyal to their players who go through bad spells and they tend to get binned off. That would be my worry for Barkley, speak to Piennar. By contrast, Rooney joined Fergie, a manager who was very good at putting his trust in young players.
Rooney moving to Utd in 2004, painful, really painful but understandable.
Barley moving to Spurs in 2017 makes absolutely no sense. He will never be loved like Harry Kane or Deli Ali and you wouldn't even say Spurs are nailed on for top 4 next season like Utd were in 2004. They are still vulnerable to losing Ali and Kane in the summer.