Saleh was released this week from a hospital in Saudi Arabia, where he was recovering from injuries suffered during a June 3 attack on a presidential compound.
There are differing reports on whether Saleh is expected to return to Yemen.
Abdel-Hafiz al-Nahari, a deputy spokesman for the ruling General People's Congress, told London's pan-Arab daily newspaper Asharq al-Awsat that Washington wanted Saleh back in Sanaa.
"The U.S. position today toward the situation in Yemen is more understanding than at any time before and they are aware that the return of the president is part of the solution, not part of the problem," he was quoted as saying.
The U.S. State Department had said political transition was being handicapped by the situation in Yemen.
Mark Toner, a spokesman for the State Department, said this week that Yemen should move "immediately" toward political transition. Asked about what would happen if Saleh returned, he said "he's not in the country right now, so we believe it can move forward without him."
Notable deaths of 2014 [PHOTOS]