The White House has also reached an agreement in principle with Argentina, Australia and Brazil, the source said on Monday.
Trump imposed a 25 percent tariff on steel imports and a 10 percent tariff on aluminum in March, but granted temporary exemptions to Canada, Mexico, Brazil, the European Union, Australia and Argentina.
The temporary exemptions were due to expire at 12.01am on Tuesday.
President Donald Trump has postponed a decision on imposing steel and aluminum tariffs on Canada, the European Union and Mexico until June 1
If it loses its exemption, the EU has said it will retaliate with its own tariffs on US goods imported to Europe, including bourbon, blue jeans and Harley-Davidson motorcycles.
Trump announced the tariffs on March 8, b