The kingdom will host the foreign ministers of Egypt, Iraq, Saudi Arabia and Syria, state news agency Petra announced.
The meeting follows a similar gathering held in Jeddah two weeks ago and “builds on the contacts that these countries made with the Syrian government”, Jordanian Foreign Ministry spokesman Sinan Majali said.
There was no immediate comment from Damascus.
Several Middle Eastern countries have held meetings with Syrian representatives in the past month as Damascus looks to emerge from its decade-long isolation.
Ankara said "constructive talks" were held with Syria last week as it looks to repair relations with its southern neighbour, while Tunisia appointed its new ambassador to Damascus on Thursday.
Foreign ministers of the Gulf Co-operation Council and Egypt, Iraq and Jordan agreed at a meet in Jeddah on April 14 that Arab states must lead the way in brokering a solution to the Syrian crisis.
Syria was suspended from the Arab League in 2011 over the government's violent crackdown on protests against President Bashar Al Assad's rule.
The protests escalated into a civil war that has claimed more than half a million lives and forced about half of the population from their homes, including millions who fled to neighbouring countries.
Support for Syria's return to the diplomatic fold has not been welcomed by all.
While Qatar attended the meeting in Jeddah, Qatari Prime Minister and Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani oppose Syria's return to the Arab League.
"There were reasons for the suspension of Syria from the Arab League and the boycott of the Syrian regime in that time and these reasons still exist," he said in an interview before flying to Saudi Arabia.
The meeting comes days before Iranian President Ebrahim Raisi is scheduled to visit Syria — the first visit by an Iranian leader since before the civil war.
Pro-government Syrian daily newspaper Al Watan reported the two-day visit would revolve around a string of agreements between the two allies, including economic accords.
Iran has provided military and economic support to Damascus, helping Mr Al Assad regain control of most of the country.