In the week that Moyes celebrated five years as Everton boss, third-placed Arsenal visit Goodison Park and it is the likes of Chelsea, Manchester United, Liverpool and the Gunners that the Scot insists he is still targeting.

Moyes said: "I have said that it is teams like Arsenal that I want this club to aspire to. Now we have a very quick chance to prove we can do it.

"I have been at Everton for five years, Arsene Wenger has been at Arsenal for over 10 years and he has built a fine club with great players and constant success.

"Maybe if I am at Everton for 10 years, that is what I could aspire to. I definitely hope so."

Moyes added: "Only ourselves and Newcastle have broken into the top four in recent years, and that was a tremendous achievement.

"But we have to build and believe we can do it again. Do we have to accept that there is nothing else for clubs like us other than avoiding relegation and trying to be best of the rest?"

When Moyes arrived at Goodison Park, avoiding relegation was the only aim.

He said: "I have had to change the mentality of the club, the players and the supporters. I want to improve and win things, but I will not tell people I can do it in one fell swoop.

"I have a five-year project that is aimed at taking us to the higher level.

"It would be great if I was here in five years celebrating 10 years at the club. You only need to look at clubs with several changes of manager, have those clubs been a big success?

"The clubs who have made strides have done it because of money, it is not down to managers. We do not have that sort of money, we may do shortly, but we are looking to develop this club and give it good foundations."

In Moyes' time at Everton his side have achieved occasional victories over Manchester United, Arsenal and Liverpool to prove such results are possible, but the Toffees manager wants those results on a regular basis.

He said: "The only thing Everton have won in recent years was the FA Cup in 1995, but are we to believe that is all there is, that we cannot win anything again?

"In the last five years we have got closer and closer to success, we have to believe we can challenge the top clubs like Arsenal.

"I have always wanted to manage a great club, and I believe I am here."

Moyes is quietly proud of what he has achieved at Everton, without the financial clout of a manager like Wenger.

He said: "It is success to say you have been a manager for five years in the Premier League, and more so at a place like Everton who have had a lot of instability.

"We have addressed that and hopefully there are signs of a good football team emerging.

"There will always be expectations at a club like Everton, and maybe what we have done in five years has heightened those expectations."

He added: "When I first came to the club the job asked of me was to avoid relegation, and that has been the case for too many years. Avoiding relegation was seen as success.

"Part of the job was changing the mentality of the club, the way people thought and get back to dizzy heights of the 1970s and 80s when the club was nearer the top than the bottom."

One Everton player, at least, is aiming to experience such levels of excitement. Portuguese midfielder Manuel Fernandes, who has made a big impact since his loan move from Benfica in January, cannot wait for the chance to face Arsenal.

He said: "You can improve quicker when you play against the best players in the world every week and this is one of those moments.

"If Benfica were in the Premiership I probably would never have left but that is football and I want to improve. Benfica is a great club but they aren't in England. England for a young player is the best place to improve."

And he agrees with the view that Arsenal are the most attractive footballing side in England.

He added: "They certainly play the better football. Maybe, though, sometimes it is better to play bad and win but that is a matter of opinion. They are definitely the best footballing team in England.

"But we need to win, because it's a home game and we have some difficult trips coming up. It is important for us to win against big teams when we are at home, not just because it is Arsenal."