At least one of those options could be the sale or merger of the 31-year-old company, according to speculation on Wall Street--speculation that company CEO/president David Stockert himself acknowledged during an Internet conference call with analysts Nov. 5. But Stockert stopped short of confirming or denying the rumor's accuracy.

"Obviously, there's a lot of rumors swirling around, and that's being fueled by this disconnect between private market pricing and REIT share prices," Stockert said during the conference call. He said he and other company officials "don't really want to participate in that conjecture and speculation and rumor."

If Post were sold or merged, it would clearly be one of the biggest transactions this year in the REIT industry, analysts say.