The protesters fear the military intends to cling to power or replace al-Bashir with another general.
Opposition leaders said on Sunday they will announce a civilian transitional council to govern the country, stepping up pressure on the military rulers.
To back up their demands, huge crowds once again gathered outside the military headquarters on Friday, chanting: "Freedom, peace and justice".
The source said military intelligence officers who searched Bashir's home found suitcases loaded with more than $351,000 and six million euros, as well as five million Sudanese pounds.
The northeast African nation is one of the world's most impoverished countries and faces an acute foreign currency shortage - a key factor which helped trigger nationwide protests against Bashir.
Bashir has been under house arrest since protests pressured the military to remove him.
The Sudanese Professionals Association, which has been spearheading the protests, said it would name members of its transitional council at a news conference at 1700 GMT on Sunday outside the army base.
It is behind the announcement of the council. Protesters demand a speedy transition to civilian rule.
"We agreed to continue negotiations to reach a solution that satisfies both the sides, so that the transfer of power will happen in a peaceful way".
"During these talks we've felt that the military council has no desire to hand over power", Rabia said.
But despite moves to hold Mr Bashir and others to account, Sudan's army does not appear to have the confidence of protesters demanding civilian rule, BBC Africa correspondent, Alastair Leithead, says.
On Sunday it said it would respond to the call for civilian rule within a week, and indicated it might favour a joint council.
The two Gulf Arab countries will deposit $500 million with the Sudanese central bank and send the rest in the form of food, medicine and petroleum products, their state news agencies said in parallel statements.
Security services found euros, dollars and Sudanese pounds totalling more than $130m (£100m).
A source in Bashir's National Congress Party said authorities arrested the acting party head Ahmed Haroun, former first vice president Ali Osman Taha, former Bashir aide Awad al-Jaz, the secretary general of the Islamic movement Al-Zubair Ahmed Hassan and former parliament speaker Ahmed Ibrahim al-Taher.