Parliament will discuss "a draft law that regulates the entry and residence of Arabs and foreigners", al-Watan said on Monday.
If approved, the law would require "any person entering or leaving Syria to hold a valid passport" which "would need to be stamped with a visa from one of Syrian diplomatic missions or consulates abroad".
Arabs and other foreigners visiting Syria will have to explain the reason for their visit and declare their place of residence in the war-torn country, in addition to proving their solvency, it said.
Those convicted of violating the law would face six months to two years in jail and a fine of 50,000 to 100,000 Syrian pounds ($350 to $700).
Anyone captured, trying to enter via an illegal crossing, will be subject to the same penalties, the report said.
Terrorists have taken over several border crossings on the frontiers with Turkey and Iraq.
Nationals of countries "in a state of war" with Syria, or that have severed diplomatic relations with Damascus during the conflict, would have to pay a higher penalty of 50,000 to 200,000 pounds ($350 to $1,400) for not having a valid visa, said the paper.
They would also be jailed for between one and three years.
Anyone caught "entering or leaving Syria illegally, or found at a border area without a valid reason" would also face a year to five years in prison, al-Watan said.
The Syrian government has repeatedly blamed violence in the country on "terrorists" entering Syria illegally. Syria has been gripped in violence since March 2011, when terrorist groups from some neighboring states and even Western countries infiltrated the war-stricken country.
NTJ/BA