The talks will examine resuming commercial agreements made prior to the US invasion of Iraq in 2003, the reopening of an oil pipeline between the two countries, and security issues.
Earlier this month, al-Maliki was criticised by Washington after he held meetings with Iranian officials.
Mahmoud Ahmadinejad, Iran's president, is planning to make his first visit to Iraq although no firm date has been set, Iran's ISNA student news agency reported on Monday.
Refugee talks
In Damascus, al-Maliki is due to discuss problems faced by 1.5 million Iraqi refugees in Syria.
The UN High Commissioner for Refugees (UNHCR) said last month that health and education services in Syria and Jordan were struggling to cope with the amount of Iraqi refugees.
An estimated 30,000 Iraqis arrive in Syria every month, something al-Shara has called an "economic, social and political burden."
"Syria has welcomed nearly two million Iraqis... and up until now there are no suggestions they will go home soon," Ath-Thawra, a state-run Syrian newspaper, said.
"Syria believes there is no alternative to [Iraqi] national reconciliation," it said, adding that "the occupation is the root of its problems."
US criticism
Syria, which has a Sunni Muslim majority, has appealed in the past to al-Maliki's Shia-led government to win over Iraq's disenchanted Sunni minority.
But al-Shara denied that Syria differed with Iran in its policy towards Iraq, insisting both governments "want an Iraq that is unified, independent, Arab and free from all occupying forces."
Since its 2003 invasion, the US has strongly criticised Syria and Iran's role in Iraq.
Washington accuses Tehran of providing weaponry to Shia armed groups and Damascus of allowing infiltration of Iraq's border by Sunni fighters, charges both governments deny.