Boston Mayor Martin Walsh is looking into what it would cost to offer partly or completely free public transit, but he is already concerned about the price tag. In an interview last Friday on WGBH’s “Boston Public Radio,” the mayor said he doesn’t outright oppose calls raised by some advocates — including Boston City Councillor, and potential mayoral challenger, Michelle Wu — to make the MBTA, or at least bus routes, free to riders, but he does not yet see a path to funding such a dramatic change.

“We are looking into what it would cost now,” Walsh said. “We want to do that now because we want to find out. But that’s an expense that the T today can’t afford.”

Calls for eliminating fares have not gained significant momentum but have grown more common since a set of MBTA rail and ferry fare hikes went into effect last summer and since ridership increased on three Lawrence bus routes the city made free in a pilot program.

Eliminating fares would force policymakers to come up with new sources of revenue. Fares represent a large portion of MBTA resources and are supplemented by state aid and community assessments. Budget-writers expect the T to bring in about $700 million from fares in fiscal year 2020, roughly a third of all revenue the transit agency will receive.

“Some European cities have free public transit,” Walsh said. “If we could come up with free public transit, that’s the way to go. The problem is, or not the problem but what the issue’s going to be, is how do you pay for it? How do you make up the money on the MBTA? We have to have that conversation. It’s easy to throw ideas out there, but when you put ideas out there, we have to back it up with how do you actually pay for this, and that’s going to be the key point here.”