Moyes has yet to be approached by Newcastle as they ponder Steve McClaren's exit and subsequent replacement and took up an invite from the Italian Football Federation to speak and discuss coaching ideas.
The 52-year-old admitted he would like to coach in Serie A one day but has his focus on a return to the Premier League.
'It was a great experience. Very technical, talking about team shapes and diagrams but all good. Could I come to Serie A? I'd like that,' he said. 'I've rejected a lot of offers from around Europe. We like Italian football, we're used to watching it in England every Sunday, ever since the days of [Diego] Maradona.
'All the Italian teams are good, and they're always good in Europe - though maybe less so in recent years, Juventus aside - and the national team is always fighting for important goals.'
Talking to Gianluca Di Marzio's website, Moyes added: 'It's a privilege to be here, I'm having fun. I've already been at Coverciano a few times, I came here with Everton when we faced Fiorentina a few years ago, but also as a young coach to learn when [Giovanni] Trapattoni was coaching here.
'I'm teaching today, but I just want to learn, there are some great coaches here today. It's important to come here and understand what it means to coach at the highest level though.
'Allegri deserved it, he had a great season last year, especially with the Champions League final. It was a great achievement, Italian football hadn't been at that level for years. They have a chance against Bayern too.'
Moyes, asked about Leicester boss Ranieri, whose team are five points clear at the top of the Premier League, said: 'He's doing a fantastic job, everyone in England wants Leicester to win the title. It's a great football story, maybe for once money won't be the key to winning, and that's a great message for all of football.
'I gave him my compliments, there's big pressure on him now in every game. There are big clubs chasing, like Arsenal, [Manchester] City and Tottenham - it'll be tough.'