Schnapp, 17, revealed in a TikTok video that the pop star sent him a message via Instagram asking him to tell Quinn to “hmu [hit me up]”.
The 29-year-old Quinn, who played Eddie Munson in the latest series of Stranger Things, has been the subject of adoration among fans of the series – including Doja.
In his TikTok video, Schnapp showed a screenshot of a fan who tweeted a photograph of Quinn and wrote: “Doja look how fine Joseph Quinn is.”
The “Kiss Me More” singer, 26, replied: “It’s f***ing criminal.”
Schnapp then showed a screenshot of his messages with Doja, which started with her writing to him: “Noah can you tell Joseph to hmu? Wait no. Does he have a girlfriend?”
He urged her to “slide into his DMs”, to which Doja replied: “I don’t know his Instagram or his Twitter. He doesn’t have a DM to slide in.”
Schnapp helped her out by sending her Quinn’s Instagram profile, adding: “Right here ma’am.”
He captioned the TikTok video: “Thirsty Doja.”
Quinn, who delivered one of the most praised lines in the recent season of the show, previously revealed that he does not use social media often.
He told Vulture in June: “My exposure to social media has been minimal. I don’t have TikTok; I have an Instagram account managed by a friend.”
Meanwhile, Millie Bobbie Brown, who plays Eleven on the series, has candidly called out its creators, the Duffer brothers, for failing to killing off many original characters.
The show’s co-creator, Matt Duffer, later responded to her criticism in an appearance on the Happy Sad Confused podcast and described the 18-year-old as “hilarious”.
He added: “Believe us, we’ve explored all options in the writing room. Just as a complete hypothetical, if you kill Mike [Finn Woldhard], it’s like… that’s a depressing… we aren’t Game of Thrones. This is Hawkins, it’s not Westeros.”
The first seven episodes of Stranger Things’ fourth season premiered on 27 May and became the second original title in Netflix history to surpass one billion hours viewed in the first four weeks of release.