The bridge is one of 14 projects selected by the Obama Administration as part of a program to create jobs and improve infrastructure.
Governor Andrew Cuomo's request came before any decision was made public on whether to replace the aging, overcrowded bridge across the Hudson River.
The governor's office said Monday that President Barack Obama invited states to submit big job-creating projects in a competition for expedited approval. Cuomo nominated the Tappan Zee project.
A spokesman said speeding environmental and other approvals would be invaluable for whatever form the project takes.
State agencies estimated in 2008 that a new bridge, depending on mass transit options, could cost between $9 and $16 billion.