Mutchler was appointed by Gov. Ed Rendell, a Democrat. Gov. Corbett, a Republican, has praised her performance in the past.
On Thursday, however, he was noncommittal.
"She's still serving and she's still working," he said at a stop in Delaware County to pitch pension reform. "A decision will be made at some point in the future."
Corbett's response comes as two of the most powerful legislative leaders, Senate Majority Leader Dominic Pileggi (R., Delaware) and Senate President Pro Tempore Joe Scarnati (R., Jefferson), took the rare step this week of sending the governor a joint letter strongly urging him to reappoint Mutchler.
"We share your often-stated goal of promoting openness and transparency at all levels of government, and believe that allowing Terry to serve a second term is a critical step in reaching that goal," the letter said.
Pileggi, author of the state's open-records law, said that under Mutchler's direction, the office has become one of the most respected in the nation.
Mutchler said she understood that her office might not be front and center on the governor's agenda, but said the ongoing uncertainty has made it difficult to hire staff, and has left her 15 staff members - most of them lawyers - unclear about the future.
Mutchler says she doesn't view her $140,000-a-year post as partisan, having clashed over open records requests with Rendell and Corbett, along with many other state and municipal officials.
"It shouldn't matter if you are a D or an R," she said. "You have to be an O, for open records."
The open-records office hears appeals of information requests by members of the public that have been denied at local or state levels.
Before the passage of the open-records law in 2008, government documents, including e-mails, were considered private unless the requester proved otherwise. The law changed the presumption so that most information is now considered public unless the government entity proves otherwise.
A journalist turned lawyer who, before coming to Pennsylvania, helped develop Illinois' open-records office, Mutchler said she has felt "like Rand McNally" over the last six years.
"We're making our own map," she said. "We've changed the direction of the flow of information in Pennsylvania."
Inquirer staff writer Allison Steele contributed to this article.