After four years with Ajax, Alvarez completed a £35m transfer to West Ham at the beginning of August, penning a five-year contract until June 2028.
The 26-year-old has since made a promising start to life at the London Stadium, making 10 appearances across all competitions including seven starts in the Premier League.
However, just two months into his career at the Hammers, Alvarez has revealed that perennial Bundesliga winners Bayern Munich were looking to sign him in the closing stages of the summer transfer window, before ultimately opting to join David Moyes's side.
Alvarez had previously been linked with a number of other clubs including Borussia Dortmund, Chelsea and Arsenal, but West Ham eventually won the race for the Mexican's signature, luring him to East London with some of the money they recouped from the sale of Declan Rice.
Alvarez has insisted that he is "very happy" to have made a "beautiful" transfer to West Ham, but he has suggested that he would be "open" to making the move to Bayern if the opportunity arose in the future.
Speaking in an interview with Sky Deutschland, as quoted by journalist Florian Plettenberg, Alvarez said: "It was a very busy summer. In the last weeks (of the transfer window), I knew about the interest from FC Bayern.
"Everything can happen. I'm always open, but at the moment, I'm really enjoying my time at West Ham. I want to play and show the people my best qualities. But in the summer, you never know what's going on.
"I'm very happy about that (transfer to West Ham). I've always mentioned that it was my dream to move to the Premier League. In my opinion, it's where the biggest competition is.
"West Ham is a great club with very nice people. As a player, it's important for me to play regularly and to get minutes. I'm playing, so I'm happy. I believe we're doing quite well in the Premier League so far."
Alvarez has also admitted that he was "very close" joining Dortmund before making the move to West Ham, adding: "I made the decision with West Ham after the option with Dortmund was down. But yes, everything was very, very close. So close.
"But I always think that certain things happen for a reason. Maybe it wasn't the moment. But I am very happy at West Ham. I made a beautiful transfer."
West Ham's new technical directors Tim Steidten was ultimately the man who persuaded Alvarez to join West Ham, with the Mexican becoming his first signing at the club since taking up his role in July.
"It was funny because [Steidten] called me and said, 'Listen, I want you for my new project. You're my first player. I know what you can give us,'" Alvarez added. "He gave me confidence and the opportunity. Then I told him, 'Tim, if you really want me, I am with you. I want to play for West Ham in the Premier League.'"
Alvarez is expected to be involved in West Ham's upcoming Europa League group-stage clash in Greece against Olympiacos on Thursday.