The Orlando (Fla.) Sentinel reported Saturday that an e-mail it obtained reveals Griffin ordered his staff to research the question. Previously, Griffin has argued against using the shuttle beyond 2010.
He has said doing so could endanger astronauts and threaten NASA's fledgling Constellation program, a system of new rockets and capsules intended to replace the shuttle.
NASA spokesman John Yembrick said the space agency has not finalized the parameters of the shuttle study.
"Our plan is still, of course, to retire the shuttle in 2010," Yembrick said.
The newspaper reported that to have money to bankroll the Constellation program, NASA must either retire the shuttle or get more money from Congress.
On his blog, Wayne Hale, a NASA deputy assistant administrator who recently was the shuttle-program manager, suggested it might be too late to postpone the shuttle retirement.
"Where does the money come from? Where do the people -- who should be working on the moon rocket -- where do they come from? We started shutting down the shuttle four years ago. That horse has left the barn," he wrote.