Inslee said sending waste to New Mexico is two to four years away. He also said a system is in place to treat the groundwater should contamination from the leaks reach it.
In the meantime, Inslee plans to push Congress to fully fund this proposal, saying "every single dollar of it is justified."
South-central Washington's Hanford Nuclear Reservation is home to 177 underground tanks, which hold toxic and radioactive waste left from decades of plutonium production for the country's nuclear weapons arsenal.
The tanks hold some 56 million gallons of waste and have long surpassed their intended 20-year lifespan. The Energy Department has said the leaking tanks could be releasing as much as 1,000 gallons a year.
State and federal officials have said the leaking materials pose no immediate threat to public safety or the environment, but the leaks raise concerns about the potential for groundwater to be contaminated and, ultimately, reach the neighboring Columbia River about 5 miles away.
Inslee has said repeatedly that Washington state has a "zero tolerance" policy for leaks.
In a letter to Inslee, the Department of Energy estimated it will have to eliminate $92 million for its Office of River Protection, which oversees efforts to empty the tanks and build a plant to treat the waste. The cuts will result in furloughs or layoffs impacting about 4,800 workers in Washington, including 2,800 contract employees dealing with tank waste and construction of a plant to treat the waste, the agency said.
Inslee spokesman David Postman said the governor's initial concern is for the workers, but he emphasized budget constraints cannot be an excuse to delay response to the leaking tanks.
The U.S. government spends some $2 billion each year on cleanup at Hanford â¿¿ one-third of its entire budget for nuclear cleanup nationally â¿¿ so the project is still in line to receive most of its usual federal funding.