The 25th Anniversary VHS set of the Trilogy (very fine product) has comments from various principals at the beginning of each movie. At the beginning of the GF tape, Puzo said that he had heard that Danny Thomas(!) was planning to buy Paramount so he could play Vito Corleone(!!) "I was disturbed by that," Puzo says, in the understatement of the year. So he got Brando's address from his agent and wrote to him, asking if he'd be interested in playing Vito. To his surprise, said Puzo, Brando wrote back immediately, expressing strong interest. But he said he'd have to wait until Paramount announced a director.
It's true that Paramount didn't want Brando (or Pacino, either). FFC accommodated Paramount by asking Brando to do a screen test for the role--nominally a humiliating thing for an actor of Brando's stature. But Brando went along with it because he wanted the role. You can see part of the screen test on "The Godfather Family," which is included in the "extras" disc of the DVD trilogy.