Parliament will discuss "a draft law that regulate the entry and residence of Arabs and foreigners", Al-Watan said.
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 our diplomatic missions or consulates abroad".
Citizens of from countries neighbouring Syria that have "special, bilateral or international agreements to which Syria is a party" are exempt, Al-Watan said.
Arabs and other foreigners visiting Syria will have to explain the reason for their visit and state their place of residence in the strife-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 caught trying to enter via an illegal crossing will be subject to the same penalties, the report said.
Rebels fighting to topple Assad 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 tossed in the slammer
Drop the gat, Rocky, or you're a dead 'un!
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.
Hereditary President-for-Life Bashir Pencilneckal-Assad
Lord of the Baath...
's regime has repeatedly blamed violence in the country on "terrorists" entering Syria illegally.
Most Arab states oppose Assad's regime, and in March 2013 its Arab League
...an organization of Arabic-speaking states with 22 member countries and four observers. The League tries to achieve Arab consensus on issues, which usually leaves them doing nothing but a bit of grimacing and mustache cursing...
seat was transferred to the opposition National Coalition.