Sudan has said any such move could undermine the peace process in Darfur and aid officials fear a potential backlash.
The Darfur investigation also could embarrass China, Sudan's close ally, just weeks before the start of the Beijing Olympics.
In the event of an arrest warrant being issued, it will be first-ever bid before The Hague-based tribunal to charge a sitting head of state with war crimes.
Genocide
The Washington Post newspaper earlier reported that the prosecutor of the ICC would seek an arrest warrant for al-Bashir, charging him with genocide and crimes against humanity, citing UN officials and diplomats.
Publicly, the United Nations has remained quiet over the issue that could pit the demands of the UN-backed ICC against UN interests in deploying a peace force in Darfur.
Ban Ki-moon, the UN secretary-general declined on Thursday to say who would be named or what the consequences might be for the struggling UN-African Union force.
Seven soldiers of the force were killed in an attack by unidentified militia on Tuesday.
"Peace without justice cannot be sustainable," he said. "I will have to assess
all the situations when there will be an announcement by the ICC."
International organisations in Sudan also tightened security on Friday, in fear of a potential violent backlash if the arrest warrant was sought.
"In light of recent security developments staff are advised to upgrade their personal security measures," an urgent security notice sent to UN staff in Khartoum said.
The notice told staff to refrain from all but essential movement over the weekend and after dark.
Security drills
The US state department withdrew all staff from the war-torn western region of Darfur, including those working for its humanitarian arm USAID, aid workers said.
UN agencies there were practising evacuation drills and might pull out all but essential staff, they added.
The UN mission in Sudan and the US embassy all declined to comment officially on security preparations.
After ICC-prompted warrants for the arrest of two Sudanese suspects last year, government-organised protests were held in Khartoum's streets.
Khartoum refused to hand over the two suspects, Ahmad Harun, a government minister, and Ali Kushayb, a militia commander.
Instead, it made Harun state minister of humanitarian affairs.
Luis Moreno-Ocampo, the chief ICC prosecutor, said last month that Sudan's "entire state apparatus" was involved in an organised campaign to attack civilians in Darfur and said he would present judges with evidence implicating senior Sudanese officials in July.
His office said he would hold a news conference on Monday when he will "summarise the evidence, the crimes and name individual(s) charged".
Judges probably will take several weeks or even months to rule on the likely application for new arrest warrants.