Sources close to Ceferin have told the BBC he has nearly 40 pledges of support from the 55 Uefa member nations.
His rival is Dutchman Michael van Praag, a member of Uefa's executive committee and the former chairman of Ajax.
A simple majority of 28 votes is required to win the election.
The victor will take on the remainder of banned Michel Platini's term of office until 2019.
Platini is set to address congress delegates before the election takes place after being granted special permission by the Fifa ethics committee to make a short speech.
The Frenchman was banned from football for four years after it was revealed he had received a Swiss francs 2m (approximately £1.6m) payment, authorised by former Fifa president Sepp Blatter, in 2011 for work he carried out for Fifa some nine years previously.
Van Praag v Ceferin: Uefa presidency Q&A
The head of the Slovenian Football Association, Aleksander Ceferin, is on course to win the Uefa presidential election in Athens on Wednesday.