It was only three years ago that Muller was a wanted man after a fine campaign with Hamburg.
The winger had scored five goals in 27 total appearances for the 2016/17 campaign, including the decisive goal that kept Hamburg in the top-flight.
Clubs had been watching Muller's progress and decided in the summer of 2017 to make a move, according to German publication Bild.
And Muller has confirmed to Tribalfootball.com that he did receive an offer to join the Hammers.
"Yeah I was close. I don't know if it was 2016 or 2017," Muller said.
"I had an offer from West Ham and I talked to them, but yeah, then I wanted to stay in Germany and play there."
Instead Muller decided to see out the final year of his contract with Hamburg, but an ACL injury suffered on the first match-day of the season sidelined him for nine months.
The club were relegated from the Bundesliga for the first-time that season and have yet to return.
And Muller says he still keeps in track of the club religiously.
"I follow every game and watch every week from Hamburg," he added. "I hope so much that come back to the first league because it's a big club.
"They have the best fans in Germany. This club has to be in the first league, I hope so."
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