Weah, who won the FIFA player of the year award and Ballon d'Or in 1995, is attempting to replace current Liberian president and Nobel prize winner Ellen Johnson Sirleaf.
Liberia's Observer newspaper reports that "the possibility of a run-off between presidential hopefuls George Weah of the Coalition for Democratic Change (CDC) and Joseph Boakai of the ruling Unity Party (UP), is becoming increasingly likely."
The term 'run-off; refers to a second round of voting in which the candidates who emerged first and second in the original round go head-to-head.
Weah, standing for the Coalition for Democratic Change, was one of 20 candidates who took part in the election. But the Observer reports that he and Joseph Boakai, of the ruling Unity Party, dominated polling and emerged far ahead of the rest of the field.
The former PSG, Monaco, Chelsea and Manchester City striker first ran for office in 2005 but was considered too inexperienced. By 2014 he was voted into the Senate.
Liberia, located in west Africa, has been plagued by political instability and brutal civil wars in the 1980s and 90s before a peace agreement in 2003. However the country still faces numerous challenges, including the fact that 85% of the population live on less than $1.90 a day.