Allardyce has come in for heavy criticism despite guiding Everton away from a relegation battle, and they currently sit in the top half of the table but 20 points behind fifth spot.
However with ambitious, rich owners and a new stadium on the way, Alladyce says everything is in place to get there one day.
"It's had major changes," Allardyce said. "It's got major changes in the ownership, and in terms of where it's going. It is making major changes because it's going to build a brand new stadium and in building that brand new stadium it builds expectation.
"A new stadium at Everton is the right thing to do and the right way forward to try to achieve everybody's desire, particularly the fans.
"With it you give the fans a better chance that this club can then compete in Europe and maybe one day even compete and get in the top four, and into the Champions' League.
"I think if Everton go to a new stadium competing in the top six or seven or even greater, then it will give more of a chance of getting towards where the fans want to go."