Obama will announce his intention during the State of the Union address Wednesday night, the newspaper said.
The decision follows Tuesday's U.S. Senate vote against creating a bipartisan commission that would have been charged with identifying ways to cut spending and increase revenue. The measure fell seven votes short of the 60 it needed to win Senate approval.
The panel Obama will appoint will be instructed to look for ways cut annual federal budget deficits but will lack any authority to force Congress to take any steps to cut spending or increase revenue, the newspaper said.
The matter of rising debt will be a central item in Obama's Wednesday night address, the Times reported.
Prior to the Senate vote Tuesday, the Congressional Budget Office projected the deficit for the fiscal year ending Sept. 30 would come to $1.3 trillion -- slightly lower than last year's annual deficit. However, the CBO said the long-term projection indicates the total debt could approximate the entire U.S. gross domestic product in 10 years.