The Post said Greenberg has been buying hundreds of thousands of New York Times shares, but an exact amount was not known.
Morgan Stanley, another large New York Times shareholder, has been pressing the company to drop the dual-class share structure that gives the Sulzberger-Ochs family voting control.
Shares of New York Times are up 6% to $24.42 in mid-day action Wednesday.
NOTE: No filing has been noted yet disclosing the purchases. If Greenberg accumulates a 5% or more stake and intends to influence the company he will be required to file a 13D.