American advisers have helped supervise the training of the Somali forces to be deployed in the offensive, the paper said.
Washington has provided covert training to Somali intelligence officers, logistical support to peacekeepers, fuel for the manoevures, intelligence on fighters' positions and money for bullets and guns, the report said.
US officials said it was part of a continuing programme to "build the capacity" of the Somali military, and that there has been no increase in military aid for the coming operations.
The New York Times report also says that Washington is using its clout as the biggest supplier of humanitarian aid to Somalia to encourage private aid agencies to move quickly into "newly liberated areas" to help civilians in an effort to make the government more popular.
The revelations follow a statement by a senior US military official that the US was considering joining a European Union effort to train a new army for Somalia's weak UN-recognised government.
Major-General Richard Sherlock, head of plans for the US Africa Command, said on Thursday there was considerable scope for co-operation with the EU training programme.
"We will look to contribute to the international effort to support Somalia's transitional government," he said.
The EU mission is part of a wider international effort to help stabilise the country.
Under the EU plan, about 200 European military instructors will start training a unit of up to 2,000 Somali troops in May at a military base in Uganda.
Somali officials have, in recent weeks, hinted that government soldiers, backed by the African Union forces, will soon attempt to wrest back control of al-Shabab-held areas of Mogadishu.
Al-Shabab controls much of Somalia and operates openly in Mogadishu, confining the forces of the government and African Union peacekeepers to a few blocks within the city.
The group wants to topple the government and impose its own strict version of sharia, Islamic law.
US military intervention in Somalia in the early 1990s, commanding a major international relief operation ended in disaster when the UN force became drawn into fighting with local commanders.
During the so-called Battle of Mogadishu in October 1993, a total of 18 US soldiers were killed in one day.