BOSTON – Two former Massachusetts governors planned to meet Wednesday with current Gov. Charlie Baker to promote an underground rail connection between North Station and South Station in Boston, adding to the pile of hoped-for improvements to the region’s strained transit system.

The idea of linking the two major transit hubs, roughly one mile apart, has been discussed on and off for decades but never pursued beyond design studies or other preliminary planning.

The former governors, Democrat Michael Dukakis and Republican William Weld, and other supporters of a North-South rail link say it would create a more modern and efficient regional transportation network. They argue it would unite the north, south and western branches of the state’s commuter rail system and provide for the possibility of uninterrupted Amtrak passenger service between Washington, D.C., and Maine.

Baker said Tuesday he viewed the meeting as a “learning opportunity” but offered no commitments.

“I’m interested in hearing what both governors … have to say,” said Baker, a Republican who once worked in Weld’s administration. “It’s incumbent upon us that we build a forward looking, five-year capital plan for state government generally and transit and transportation stuff in particular, which is what this would be a discussion about.”

Dukakis and Weld have not said what they think the project would cost but suggested in an op-ed article in The Boston Globe last month that it could ease congestion at both North and South stations, eliminating the need for costly expansions of them.

The former governors said automated tunnel-boring machines would cost less and create far fewer disruptions than occurred during the Big Dig highway project.

But Wednesday’s meeting comes just weeks after a fiscal control board that is overseeing the Massachusetts Bay Transportation Authority was told that another major project, the expansion of the Green Line to Somerville and Medford, could cost up to $1 billion more than originally planned.

The MBTA is also still reeling from massive breakdowns that brought portions of the aging system to a halt during severe weather last winter. The agency recently revealed that its State of Good Repair backlog had grown to $7.3 billion.

Dukakis served three terms as governor in the 1970s and 1980s and has been an ardent mass transit supporter. As governor, he often rode the Green Line from his Brookline home to the Statehouse and served on Amtrak’s board after leaving office. He was the 1988 Democratic nominee for president.

Weld succeeded Dukakis as governor and also supported the rail link while in office.