Mayor Bill de Blasio’s administration is offering more than $2 billion for the Metropolitan Transportation Authority’s five-year capital plan, according to people familiar with the matter, amid negotiations with state officials about the transit agency.

The city had promised $657 million but is ramping up its total offer—provided the state meets certain conditions—in an attempt to end a fight that has dragged on for months, according to these people.

Negotiations are under way on how much more authority city officials would have on the system’s operations if the city contributed the larger amount, these people said.

City officials have internally looked at a range of options in a plan to give the state agency more than $2 billion, including potentially using money from sales taxes from for-hire vehicles, such as taxis and those driven for car services, such as Uber and Lyft, according to people familiar with the matter. But a City Hall spokeswoman said revenue from the for-hire-vehicle industry hasn’t been part of negotiations on the MTA’s capital plan.

A deal could ease tension between Mr. de Blasio and Gov. Andrew Cuomo, Democrats who have warred in recent months on a number of issues. It also would bring some relief to the MTA, where major subway and other repair projects have slowed as it seeks a $30 billion capital plan that would last until 2019.