The sources, who spoke on condition of anonymity, said the United States also may lay out plans to impose additional US sanctions on Syria, whose government has engaged in a brutal crackdown against protesters seeking an end to the 41-year rule by Assad and his father, Hafez al-Assad.
The sources said that the US appeal could come on Thursday and would quickly be followed by similar calls from others, notably the EU.
The EU first imposed sanctions on President Assad last May, to pressure him to end his brutal crackdown on dissent. Foreign ministers agreed at that meeting in Brussels to add Mr Assad and nine other officials to a list affected by travel bans and asset freezes.
Both the EU and the US have been edging closer to an explicit call for Assad to go since Syrian protesters began to demonstrate against his rule in March, inspired by revolts that toppled autocratic rulers in Tunisia and Egypt earlier this year.
The United States held off initially in the hope that Assad might change course and embrace democratic reforms, a possibility that US officials appear to have given up on.
As recently as last week, however, US officials said President Barack Obama was leaning toward an explicit call for Assad's departure, but they made clear they wanted other nations to make a similar appeal.
Military operations against protesters stopped?
The United Nations said late yesterday (17 August) that Assad had told UN Secretary-General Ban Ki-moon that military and police operations against protesters had stopped.
In a phone call with Assad, Ban "expressed alarm at the latest reports of continued widespread violations of human rights and excessive use of force by Syrian security forces against civilians across Syria, including in the Al Ramel district of Lattakia, home to several thousand Palestinian refugees," the United Nations said in a statement.
The government's crackdown in Syria is estimated to have killed at least 2,000 civilians. The authorities appear to have accelerated their efforts to crush the protests in the last few weeks.
Syrian troops held hundreds of people in a stadium in the port city of Latakia on Wednesday, residents said. They said Syrian forces raided houses in a Sunni area of the besieged city, arresting hundreds of people and taking them to a stadium after a four-day tank assault to crush protests.
Latakia is of particular significance to Assad, who is from Syria's minority Alawite community. Assad comes from a village to the southeast, where his father is buried, and his family, along with friends, control Latakia's port and its finances.
In an interview with CBS Evening News last week, US Secretary of State Hillary Clinton made clear that the United States wanted other nations to also demand Assad's departure and to take concrete actions against the Assad regime.
Obama consulted on Saturday with Saudi King Abdullah and British Prime Minister David Cameron. In both cases, the first specific topic mentioned in the White House's summaries of the calls was Syria.
EurActiv with Reuters