But not just yet. And he doesn't want to make too much of the whole gangster angle.
"I had the left-hand corner of the 'Hollywood Squares' all lined up, and then [executive producer] Mitch [Glazer] called," Caan joked.
Sonny Corleone and Sy Berman, the character Caan plays in "Magic City," are both mobsters. But the similarities end there. Sy is much older than Sonny; he's Jewish, not Italian; and he's based in Havana.
Although any similarity between Sy and real-life gangsters isn't entirely coincidental.
"I remember eating at Wolfie's in the 10th grade and being told to be quiet because Meyer Lansky was in the next booth behind us." Glazer said. "And we were quiet instantly, I might add. So that world of seeing Meyer walk his dog was part of how I grew up."
He used that as the basis for "Magic City." Jeffrey Dean Morgan stars as Ike Evans, the proprietor of the Miramar Playa Hotel, who wishes he hadn't gotten in bed with the mob.
Ike is still trying to disengage from Ben "The Butcher" Diamond (Danny Huston), and that hasn't been going well. So in Season 2, he's going over Diamond's head to his mob superior, Sy Berman.
"For Ike, this whole season really breaks down to him wanting to rid himself of Ben Diamond," Morgan said. "And then probably Sy Berman, although he kind of learns to play the two against each other in sort of an odd way."
Caan doesn't want to draw parallels between Sy and Sonny, but Glazer is happy to do so.
"To put him in this world, in this time, I mean, it felt fated," he said. "There are moments on set that are actually surreal this season for me. To see Jimmy playing this character, Sy Berman, and saying this dialogue in this kind of familiar world was spectacular, and I loved every second of it."
So did Caan, but not because he was back in the Mafia.
"Listen, the truth of the matter is I'm at the point where I care very much about what I do," he said. "I still try to maintain a little bit of integrity."
And he thought "Magic City" was "well written and beautifully shot and something that I thought would be a lot of fun in a creative way, and it was. No, I really didn't have any specific reason other than it was good."
Scott D. Pierce covers television for The Salt Lake Tribune. Email him at spierce@ sltrib.com; follow him on Twitter @ScottDPierce.