According to a CBC News report, other delegates attending the discussions include members of secular opposition parties, independent legal experts, the representative of the opposition, Mohamed El Baradei, and business tycoon Naguib Sawiris.
The talks are taking place even as mass demonstrations continued for a 13th day to press for the ouster of President Hosni Mubarak.
The officially banned organization said in a statement early Sunday it would meet with Suleiman to press its "legitimate and just demands."
The negotiations marked the first time the Muslim Brotherhood has held direct talks with the government.
Senior Brotherhood leader Mohammed Mursi said his representatives would be sticking to the protesters' main condition that Mubarak step down after nearly 30 years of authoritarian rule.
Opposition leaders from other groups met with Suleiman on Saturday but said there was no breakthrough.
Senior government figures argue only that the president has the power to make the changes necessary to enable a free and fair election for his successor.
Mubarak has said he would not run for the presidency again in elections slated for September, but has insisted he will serve out the remaining seven months of his current term to supervise a peaceful transfer of power.
Muslim Brotherhood spokesman Assam el-Aryan said his party won't contest the next election, but it will help with the transition of power. (ANI)