City and state officials are negotiating with JPMorgan Chase over a potential deal in which the nation’s largest bank would build a vast $6.5 billion corporate campus with two high-rise towers in the new commercial district on the Far West Side of Manhattan.

The talks, which involve one of the largest real estate complexes for a single company in New York City history and a large package of incentives for Chase, have reached a feverish state after nearly falling apart this week.

The negotiations are so delicate that few people are willing to discuss them publicly for fear of alienating one side or another.

But a deal with the bank poses political risks for both the state and the city. Chase had initially sought, by one account, more than $1 billion in concessions from the city and the state while it continues to pare its payroll in the city. According to executives and officials, Chase wants to build the two towers — whose total space would be the equivalent of about two Empire State Buildings — at Hudson Yards on the north side of 33rd Street, between 10th and 11th Avenues. They would become home to 16,000 employees.