Einhorn said he suggested to Apple an initial preferred share distribution, where dividends could be funded on an ongoing basis by a relatively small percentage of the company's operating cash flow.
"It is better than a big stock buyback because it doesn't deplete the company's cash right away, which the company seems to want to keep," Einhorn said earlier on Thursday.
Apple had $137.1 billion in cash, short-term and long-term marketable securities at the end of last year, but more than $94 billion in that cash is parked overseas.
Einhorn told Reuters that Apple Chief Financial Officer Peter Oppenheimer and his advisers rejected his idea in September 2012. He added the company then refused to withdraw a proposal - outlined in Apple's annual proxy statement - to eliminate preferred stock from its charter.
"We saw that the proxy came out and we saw they were planning to get rid of preferred - and then, we said, 'Wait a minute, we are not going to be able to bring this up again in a good way if we allow them to do this,'" Einhorn said. "So we should contest it now."
Greenlight sued to block the measure, asking a federal court in Manhattan to bar Apple from certifying votes cast in its favor.
Einhorn said: "When I discussed this with Tim Cook, and actually, the conversation has been going on for the last couple of weeks, he said that he wasn't familiar with my previous conversations with Peter Oppenheimer and whoever Peter Oppenheimer's advisers were. I was surprised by that."
Einhorn said Cook is receptive to his proposals and added that Cook's advisers "want to come and meet with me."
© Thomson Reuters 2013