The Arab League suspended Syria's membership in 2011 following President Bashar Al Assad's crackdown on uprisings that evolved into a 12-year civil war.
Mr Safadi said Syria had enough votes among the group's 22 members to regain its seat.
“The return to the Arab League will be symbolic … but ultimately in order for us to really end it [the crisis], we will have to make sure that the whole international community is on board, because at the end of the day there are sanctions, European sanctions, American sanctions, and there’s going to be a tremendous need for a global effort for reconstruction,” he said in an interview with CNN.
He added the return is “only a very humble beginning of what will be a very long and difficult and challenging process, given the complexity of the crisis after 12 years of conflict”.
Arab League ministers are set to meet in Cairo on Sunday to discuss Syria's return to the fold amid a regional push to normalise ties with Mr Assad that included a regional trip by Syrian Foreign Minister Faisal Mekdad to Saudi Arabia last month.
Mr Mekdad also met Arab ministers in Amman on Monday, as part of Jordan's initiative to get Damascus to negotiate a peace plan which lays a road map to end the conflict.
Mr Safadi said Syria's readiness to make real progress in resolving the conflict would help it win the crucial Arab support to lobby for an eventual end of western sanctions that are a major impediment to launching a major reconstruction effort.
Agencies contributed to this report