The high constitutional court has notified parliament that 44 Syrians have so far submitted their names ahead of Wednesday's deadline, according to the official SANA news agency.
They still need to garner support from at least 35 members of the 250-seat parliament, which is dominated by President Bashar al-Assad's Baath party and with lawmakers only allowed to endorse one candidate.
The May 26 election would be the second to be held since the start of the 10-year-long foreign-backed militancy that has killed more than 388,000 people and forced more than half of Syria's pre-war population from their homes.
With the exception of Assad, who has been in power for 21 years, the contenders are mostly little-known figures who are unlikely to mount a serious challenge.
The pro-government Al-Watan newspaper said parliament will likely hold the vote by Wednesday evening, after the high constitutional court stops receiving applications from presidential hopefuls.
But it remains unclear when parliament will announce the final list of approved candidates for the ballot.