The 42-year-old actor discussed the possibility in an interview with the The HFPA in Conversation podcast published Wednesday.
Quinto, who plays Spock in the Star Trek reboot films, said working with Tarantino would be an "amazing" experience.
"There's nothing concrete I could give you other than I think all of us would love to come back and do another film, particularly with Quentin," the star said. "What an amazing experience that would be not only for us, but for fans and for audiences to see his take."
"He's just an undisputed genius filmmaker and amazing storyteller. And I think to give his perspective on these characters and this world would be a delight for everybody involved and everybody who got to experience it," he added. "So yeah, we're really open to it, and I know conversations are being had, but not with me at this point, so we'll see what happens."
Tarantino gave an update on the project in the July issue of Empire. He said he has a script for the potential film, which would be R-rated if he signs on as director.
"It's an R-rated movie," Tarantino told the magazine. "If I do it, it'll be R-rated."
"There's a script that exists for it now. I need to weigh in on it, but I haven't been able to do that yet," he said.
Quinto has portrayed Spock in Star Trek (2009), Star Trek into Darkness (2013) and Star Trek Beyond (2016). The films co-star Chris Pine as Kirk, Karl Urban as Bones, Simon Pegg as Scotty and Zoe Saldana as Uhura.
Quinto stars in the new AMC series NOS4A2, which debuted this month. Tarantino's new film, Once Upon a Time in Hollywood, opens in theaters July 26.