"Communication with Syria is improving and is on its way to being entirely restored to what it used to be," the official told AFP, requesting anonymity.
Hamas leaders have made multiple recent visits to Syria, the official said, adding: "Syria supports the Palestinian people and cause, and Hamas is devoted to its relationship with Syria and all Arab countries."
Syrian President Bashar al-Assad's government declined to comment on reports of warming ties.
Assad's regime and Hamas, both staunch foes of Israel, had been firmly allied until the outbreak of the Syrian conflict in 2011, when the Palestinian group publicly backed those fighting to overthrow the government in Damascus.
The rupture that followed saw Hamas abandon its headquarters in the Syrian capital, where the group's former chief Khaled Meshal had lived for many years.
Top Hamas officials subsequently relocated to Doha and Istanbul.
Hamas has voiced anger over a recent diplomatic rapprochement between Turkey and Israel.
The breakdown of Hamas-Syrian relations also angered their common ally Iran, which remains a major backer of armed groups in Gaza, a Palestinian territory of roughly 2.3 million people blockaded by Israel since 2007.
Meanwhile, Hamas leader Ismail Haniyeh arrived in Beirut on Tuesday, for meetings aimed at "strengthening cooperation and fraternity between the Palestinian and the Lebanese people", a Hamas statement said.
There was no immediate indication that Haniyeh's visit to was tied to the Syrian outreach.
