Mr. de Blasio said he liked the plan because it relies largely on private financing as part of a public-private partnership.

“It’s the best idea I’ve heard so far,” the mayor told reporters, though he said he was reluctant to commit significant direct funding from the city.

On Thursday, Mr. de Blasio announced his nominee to be the next leader of the city agency that oversees the taxi industry: Aloysee Heredia Jarmoszuk, who currently serves as chief of staff to the deputy mayor for operations. The City Council failed to approve the previous official he nominated for the job.

Mr. de Blasio could be pushed to spend elsewhere. Leaders at the Metropolitan Transportation Authority, which oversees the city’s subway and buses, have also called on the city to pay $3 billion to fix the transit system in the coming years. Funding for a taxi bailout or new subway spending was not included in the mayor’s preliminary budget.

The city’s last budget was $92.8 billion and included spending increases on things like providing social workers at city schools and a program to boost participation in the federal census. The previous budget included funding for discounted subway and bus fares for some of the poorest New Yorkers.

City officials attributed $1.6 billion of the growth in the preliminary budget to the settling of outstanding labor union contracts and said it would cost $175 million to implement changes related to bail and discovery reform.

Scott M. Stringer, the city comptroller and a mayoral candidate in 2021, said that Mr. de Blasio must protect the city from leaders in Albany who frequently target New York City’s budget when the state budget is in peril.