David Moyes has offered to give Everton every assistance in the search for his replacement as manager at Goodison Park.

The fact the Scot is leaving for Manchester United at the end of the season has not soured his relationship with Bill Kenwright, the chairman, and Moyes' own predecessor, Walter Smith, had a role in his appointment.

"I'll help Everton as much as I possibly can," said Moyes. "Walter Smith recommended me for the job here and if there is anything I can do to help Bill Kenwright with what happens next I will be more than happy to do so. It is a great opportunity.

"Everton are a well-run club and we don't get ourselves into too much trouble. There is a brilliant training ground and a great set of players with a terrific attitude. Whoever comes in is coming into a really good environment."

Moyes gives Smith credit for stabilising a club that had several times flirted with relegation, but the 50-year-old, in his 11 years at Everton, built on that to ensure they were consistently pushing towards the top end of the table.

They would have been strong favourites to land a Europa League spot this season, and still stand an outside chance, had clubs from outside the top five – Swansea and Wigan – not won the Capital One Cup and reached the FA Cup final respectively. "When I took over, we were bobbing along not far off the bottom of the Premier League," Moyes said. "Now, it is a club that, on Sunday, will still be competing to be in Europe. That is a big thing."

It is also one of the reasons why there was never any real doubt Moyes would remain in charge for the final two games of the campaign, despite announcing he was joining a club Everton fans have not always been well disposed towards.

The last player to make the switch to Old Trafford from Goodison was Wayne Rooney and he received tough receptions for several years when he returned. Moyes hopes there will be no backlash from the supporters at Everton's home game against West Ham tomorrow. "Hopefully, on Sunday, the fans will react in the same way they did when I first stepped through the door," he said. "You can never tell with football fans. They support their team and I would understand it if they weren't happy.

"But I will be standing in the same position as I always have done, trying to see if we can keep everything focused and moving in the right direction. The fans have always been great to me. It's not normal nowadays that a manager stays in their job for 11 years. If I hadn't had their backing, it wouldn't have happened."