The then manager of Chelsea, Thomas Tuchel, is now keen to link up with Alvarez as he prepares for his first full season in charge of Bayern.
Despite missing training in an attempt to force a move away to Chelsea, Alvarez has remained a key player for his current employers this term, making 41 appearances across all competitions.
However, the 25-year-old has reaffirmed his desire to secure a move to a bigger club in the future while reflecting on his failed move to Chelsea.
“There was interest from Chelsea,” Alvarez told ESPN. “Nobody expected that they would make another offer – Ajax really couldn’t do anything.
“They didn’t have a player in my position. Of course, I fought as far as I could.
“I didn’t want to do that too much because I know the responsibility I have within the club.
“I am very disappointed, but I’m convinced that sooner or later a big club will come for me.”
With Ajax set to miss out on next season’s Champions League, Alvarez could be set for a move away next summer.
Bayern are not short of competition in their pursuit of Alvarez thanks to Dortmund’s interest in the Mexican.
The two sides are currently embroiled in a tough battle for the Bundesliga crown heading into the final two games of the season.
Bayern are top of the pile by one point as things stand and could potentially secure the title this weekend if results go their way.