- Last Updated on 25.05.2018
Mr Wenger said: "I would like to congratulate one of my former players, who became president of Liberia."
He coached Mr Weah at French club Monaco in the 1990s.
Mr Weah was among 20 presidential candidates in Tuesday's election.
The former Fifa World Footballer of the Year failed in his two previous attempts but is one of the front-runners to replace President Ellen Johnson Sirleaf.
However, most analysts expect it to go to a second round, as a candidate needs more than 50% of the votes for outright victory.
False reports of Mr Weah's victory about have been circulating on social media but it is not clear why Wenger thought he had won.
"It is not often that you have a former player who becomes a president of a country," Wenger said.
"Well done George and I would say just for him to keep his enthusiasm and his desire to learn and to win," he added.
Official results have still not been announced even though the head of the National Elections Commission (NEC), Jerome Kokoya, had told the BBC that he expected the first results to be announced by 23:00 GMT on election night.
One of Liberia's leading political parties, the Liberty Party, has called for a halt in announcing results, citing alleged irregularities.
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