Iraola said Moyes was one of the managers in the Premier League that he was good friends with, and they met for dinner when both were in the USA for the Summer Series in preseason.
The Basque boss has experience of a stadium move when he was a player.
He was a part of the Athletic Club squad that moved into the ‘new’ San Mames out of the ‘old’ stadium of the same name in 2013.
Iraola said Moyes had confessed to worrying about the move from Goodison Park, where Everton had been since 1892, and into their new ground at Bramley-Moore Dock.
“It's curious because I was talking to David Moyes about this thing because we were together in the preseason summer series there in America, and we had the chance to have one dinner together and talked about football and different things,” Iraola told the Daily Echo.
A general view of the stadium ahead of the Premier League match at the Hill Dickinson Stadium, Liverpool. (Image: Peter Byrne/PA Wire)
“He was telling me that he was a little bit worried because this move to a new stadium, losing everything that Goodison was about, and there was some uncertainty and he didn't know how it will develop.
“And I told him, I moved in Athletic Club, massive stadium, San Mamés, historic with all the atmosphere to a, same place, but a new stadium, like much more modern.
“And we were worried also.
“I remember the first year we got into the Champions League with these same question marks and I told him you are going to be fine because everyone will be excited, everyone will push first season and you will be fine.
“They are being very fine and I don't know if he will remember but we were talking about this in preseason, yes.”
Iraola said he had enjoyed spending the time with Moyes, as they don’t often get the chance to do that during the season.
Everton manager David Moyes and Bournemouth manager Andoni Iraola ahead of the Premier League match at the Vitality Stadium, Bournemouth. (Image: Andrew Matthews/PA Wire)
“I think it was a dinner after we had some meeting with the referees,” he said.
“They explained the new rules, how they want the football to evolve, and they ask you some opinions.
“And it was nice also to chat with the refs. And after we had, I remember it was Graham Potter, Rubén Amorín, and we were chatting together.
“It was really nice because normally during the season you don't have time to spend with them.
“And you don't tell a lot of secrets about your team, but it was a nice moment for everyone, for me at least.”