Gibson turns down a Scorsese role … again?

It seems like, every time he directs a movie of his own, Mel Gibson tells someone he turned down a role in a Martin Scorsese flick.

In an interview with Raymond Arroyo on the set of The Passion of the Christ (2004), he claimed that Scorsese had offered him the part of Jesus in The Last Temptation of Christ (1988). Now, with Apocalypto only nine days away, he tells Entertainment Weekly:

You’re identified primarily as a director now. Have you decided to give up acting altogether?
I haven’t resigned or anything. [But I did it] for 30 years…. Martin Scorsese sent me the script from the last film he did, The Departed. I thought it was fantastic. I was like, ”S—, how come you always give me the good script when I’m about to go into production?” But I enjoy making movies more than acting. . . .

So which part was Gibson up for in that film? The evil, insane Jack Nicholson role? The devoutly Catholic Martin Sheen role? The profane, no-nonsense police chief played by Alec Baldwin?

UPDATE: For Gibson’s account of how Scorsese offered him the part of Jesus while they were staying in the same hotel in London, listen to this audio file between the 24- and 26-minute marks.