Days after MBTA General Manager Steve Poftak announced his resignation, several names are already being floated for his replacement.

“I do think the general manager job at the MBTA is the hardest job in state government and whoever has that job is going to need to earn back the trust of riders, one ride at a time,” said Chris Dempsey, a former assistant secretary of transportation for Massachusetts who has been mentioned in some of those conversations.

When asked if he was interested in the job, Dempsey didn’t rule it out, but said that at this moment, he is recovering from “a bruising campaign” against Diana DiZoglio, who defeated him in the Democratic primary for state auditor, and is looking forward to his honeymoon at the end of the month.

“It’s attractive to someone who’s looking for a challenge, that’s for sure, because it’s a very challenging role,” Dempsey said of the $300,000-plus position. “I think a new administration will bring a fresh opportunity and fresh perspective on the MBTA and what it needs.”

Dempsey, the former director of advocacy group Transportation for Massachusetts, is among a handful of names making the rounds as potential candidates for the GM position, which will be appointed by the next governor, according to a series of interviews the Herald conducted this week.

Dion Stubbs, a retired former MBTA chief operating officer who works as general manager of Valley Metro Light Rail in Phoenix, Ariz., has also been mentioned. In terms of internal candidates, Deputy General Manager Jeffrey Gonneville would be next in line.

But the name that came up the most was Monica Tibbits-Nutt, a former vice chair of the MBTA Fiscal and Management Control Board who took over that role when Poftak was elevated to the general manager position in 2019.

Tibbits-Nutt, who did not respond to a request for comment, is also a past member of the MassDOT Board of Directors and is currently the executive director of the 128 Business Council, one of the largest transportation providers in the state.

MBTA Advisory Board Executive Director Brian Kane said it’s up to the next governor, in terms of whether Democrat and frontrunner Maura Healey or Republican Geoff Diehl wants to appoint a GM right away or have an interim leadership period while a search is conducted.

When asked about Tibbits-Nutt, TransitMatters Executive Director Jarred Johnson said she brought expertise to the MBTA board, but was also an advocate, particularly in getting the T to take bus service more seriously.

“I think she’d be great,” Johnson said. “I think it’s definitely helpful to have some local experience, but still be far enough away from at least the recent troubles.”

Of Dempsey, Johnson said a similar case could be made, that he has experience with the MBTA, in Massachusetts politics, and is very in tune with issues facing the transit system.

A Healey spokesperson said the campaign had no comment, when asked if a nationwide search would be conducted for the next general manager, or if the appointment would be local. The Diehl campaign did not respond to a request for comment.

But Stacy Thompson, LivableStreets executive director, said her personal preference would be to stick with someone local.

“I wouldn’t write someone off who isn’t from the Boston area, but it’s valuable to have someone who knows people and who people respect,” she said.

She would like to see the next governor look at candidates with prior knowledge of the system, who weren’t there “when problems were going on, but still understand the MBTA.”

Thompson cited the problems Poftak’s predecessor, Luis Ramirez, who lasted just 15 months as general manager before it was “mutually agreed” upon that he should leave, encountered after stepping into the role as an outsider from Texas.

“He walked in and he didn’t know anyone,” Thompson said. “He didn’t have bad intentions, but it was very hard to get up to speed.”

State Rep. William Straus, who co-chairs the Joint Committee on Transportation, said the next governor should be open to either, but having experience with Massachusetts does help.

“Somebody who doesn’t have the experience of dealing with the personalities and the individuals here often does have a harder time,” Straus said. “Certainly I’ve seen that with not Steve Poftak, but the predecessor from Texas who immediately had to get to know people before he could even consider doing the job.”

However, Joseph Aiello, chair of the former Fiscal and Management Control Board, said he was “agnostic” on the matter. Experience in the transit industry and being able to navigate the complexities of metro Boston politics is important, he said, but ultimately it’s about how a general manager optimizes those qualities.

“There are just people who leap at this opportunity, who are quite good at it,” Aiello said. “Whether that person is local, not local, I will say that the new governor has some good choices before her,” he said.

Straus said he expects a decision will be made soon after Tuesday’s election, which would put MassDOT Secretary and CEO Jamey Tesler in the unique position of appointing a general manager for an administration he will likely not be a part of.

Poftak’s last day is Jan. 3, two days before the next governor is sworn in.

“The statute makes it clear that it’s the secretary that appoints the general manager, but I think it’s safe to say if there were an appointment announced before Jan. 3 by Secretary Tesler, it would not be done in a vacuum, without the strong input from the next governor,” Straus said.

While a number of names were floated, the general consensus was that the next general manager “should be focused on safety first and foremost,” as state Sen. Brendan Crighton, co-chair of the Joint Committee on Transportation, put it.

However Charlie Chieppo, senior fellow at Pioneer Institute, said the focus should also be on basic things like fixing a pension system that is bankrupting the T, but he said that will never happen because of political reasons and it would “draw the ire of the Carmen’s” and other MBTA unions.

“There’s been a mix of local and real national figures who came in,” Chieppo said. “Who gets this job and who does this job next is important. But just as important is the commitment of elected officials to do the hard job and fix it. That is just where I’m not optimistic.”