Graham spoke about the mysterious role while on the Pound for Pound podcast, saying: "I was supposed to be starting Peaky Blinders but that has been put on hold indefinitely.
"Luckily I was in a really good position where I was going to go from job to job for the next three years – my agent spent a lot of time putting that together – and obviously the rug just got pulled from under our feet."
The BBC declined RadioTimes.com's request for comment, but it doesn't sound like we'll be seeing Graham enter the Birmingham gangland fold any time soon.
Fans have wanted Graham to join the show ever since Al Capone – a character he portrayed on HBO's Boardwalk Empire – was hinted at in Peaky Blinders season four.
Creator Steven Knight finally confirmed they were in talks to bring Graham on during an Obsessed With... Peaky Blinders podcast appearance back in summer 2019, but said he would not be playing Capone.
"Not Al Capone – I didn't want to go west," he explained. "Because it's a minefield once you go into Chicago gangsters. I refer to him last series, but I didn't want to go into that."
Peaky Blinders seasons 1-5 are currently available to watch on Netflix. Looking for your next lockdown watch? Check out our round-up of best Netflix TV series.