Muallem is to deliver an invitation to Lebanese President Michel Sleiman from his Syrian counterpart Bashar al-Assad to visit Damascus, a trip the Lebanese press said would take place within a week or 10 days.
Lebanon and Syria said last weekend that they had agreed to establish diplomatic relations, opening embassies in both capitals for the first time since their independence from French colonial rule more than 60 years ago.
"It is expected that the question of diplomatic relations will be raised during the visit. We hope it will mark a new step in Syrian-Lebanese ties," said Syria's Al-Watan newspaper, which is close to the government.
It said that during his visit Muallem would discuss "ways of improving relations given the favourable circumstances with the election of a consensus president in Lebanon and the formation of a national unity government."
Sleiman was elected president and a new government formed under a May deal between the anti-Syrian ruling majority and the Damascus-backed opposition to end a drawn-out political crisis that had boiled over into deadly violence and pushed Lebanon to the brink of a new civil war.
Syria continues to wield considerable influence in Lebanon, although it pulled out its troops in the aftermath of the killing of Lebanese ex-prime minister Rafiq Hariri in 2005, ending a near 30-year presence.
Damascus was widely blamed for the bomb blast that killed Hariri, but denies involvement and has protested at plans for a UN tribunal to try suspects in the murder, which triggered several years of instability in Lebanon.
The plans to establish ties were announced at a summit in France to launch a Mediterranean Union which was attended by Assad, marking his return to the international stage after several years of diplomatic isolation.
Franco-Syrian ties went into deep freeze after the assassination of Hariri, who was a personal friend of French President Nicolas Sarkozy's predecessor Jacques Chirac.
In a further sign of improving ties, Sarkozy announced he would visit Damascus in September.