Marine Gen. John R. Allen has prepared a request for the troops but has yet to submit it to the Pentagon, the Los Angeles Times reported.
The request is a sign the United States and its allies hope to speed the process of handing over combat operations to the Afghans as troops prepare to withdraw.
Greater emphasis on the training role could keep more U.S. troops on bases next year and reduce U.S. military casualties before the presidential elections in November, the Times said. President Barack Obama's Afghanistan policy already is a 2012 election issue.
The mid-level officers and senior enlisted troops Allen is requesting would lead hundreds of new adviser teams to be assigned next year to Afghan units fighting the Taliban, officials said.
The move is part of the Obama administration's strategy to ensure Afghan forces are prepared to battle the militants by 2014, when U.S. combat units are to withdraw.
Allen and others favor giving the Afghan army the lead role in fighting sooner while numerous U.S. troops still in the country could come to the aid of the Afghans, if needed.
The Times also noted support for keeping combat troops in Afghanistan for three more years has declined among NATO countries, giving the Obama administration more incentive to speed the transition to Afghan forces.
"Our top priority right now is building" the Afghan army and police, a senior U.S. general involved in the discussion told the Times. But the general said: "It's a perilous path we're on right now. ... The Afghans can't carry the load by themselves."
Obama has ordered withdrawal of 30,000 troops from Afghanistan by September, leaving about 68,000 U.S. troops in the country.