Gov. Charlie Baker speaks at a press conference on March 17, telling reporters that “without question, we are likely to have some very tough days ahead of us.” Photo by Sam Doran | State House News Service

Gov. Charlie Baker said Tuesday that he would “probably not” sign a law reviving rent control if the legislature were to send one to his desk, making clear the challenges that Boston mayoral frontrunner Michelle Wu could face in making her agenda a reality if she becomes mayor.

Rent control was outlawed in Massachusetts by a 1994 ballot question, but the idea of capping price increases to keep rents affordable has figured into the mayoral campaign in Boston. Wu supports the policy but candidate Annissa Essaibi George does not.

Enacting rent control in Boston would require approval from the legislature and governor.

During an appearance Tuesday afternoon on GBH Radio, Baker told co-hosts Jim Braude and Margery Eagan that he would “probably not” sign a home rule petition from Boston that sought to reimpose a form of rent control and said the experience he had living in Boston in the age of rent control informs his thinking.

“I’m going to leave the door open a little bit because maybe there’s something that could be done to deal with this,” Baker said, pointing to the issue of fairness and the effects rent control could have on housing development.

The governor added, “I lived for a bunch of years in Boston paying market rent when I was a young person next to two apartments that had older folks in them that made more than me who paid about half what I paid in rent because their apartments were rent-controlled and mine wasn’t. As we all know, that was in many ways one of the biggest issues people have with rent control generally, which is basically it did not treat everybody the same and your income had nothing to do with whether or not you had a rent-controlled apartment.”

A recent Suffolk University poll taken for the Boston Globe and NBC10 found that 59 percent of the 500 likely Boston voters surveyed said they support the idea of rent control in Boston.

In an interview with Banker & Tradesman’s editorial board earlier this month, Wu said she envisioned a proposal similar to Oregon’s “rent stabilization” system, where landlords are allowed to increase rent 7 percent in any 12-month period, plus inflation.