The 74-year-old actor, who owns a series of restaurants in Los Angeles, said when Bourdain turned up at Trejo's Cantina it felt like "getting visited by the Pope".
"It was the first time I've ever heard the whole restaurant quiet. We didn't even have to say, 'Rolling'. Everyone was just quiet, and they wanted to hear what he said. He was just so gracious, and he didn't say a bad thing," he added.
The restaurant had featured on a Los Angeles episode of "Parts Unknown" in April 2017.
Another of the "Machete" actor's restaurant, Trejo's Tacos, which opened in 2016, also featured in the season nine premiere of "Parts Unknown".
Trejo said Bourdain loved his cauliflower tacos and jackfruit.
"I was so proud. You do something and the Pope tells you that it's good, it almost brings you to tears," Trejo said, adding that Bourdain "made me feel good that I was in the restaurant business".
Trejo, after learning of Bourdain's death, had also tweeted his condolences, accompanied with suicide prevention lifeline number.
"Anthony the entire world will miss you, this is a tremendous loss. You were one of the nicest men I've ever met. Please, if someone you know is suffering, step in, say something, offer out your hand. My heart goes out to your family," Trejo had tweeted.
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