The American forward played 17 times on loan for Celtic last season, and was popular with many Bhoys fans.
Weah was brought to Celtic in January by Brendan Rodgers, and went on to score or make five goals in 17 games for the Bhoys.
But his temporary spell was cut short early last month - per the instruction of Neil Lennon, according to the player - leaving a return to Celtic Park unlikely.
And Weah is now expected to remain in France, after Lille reportedly agreed a €10 million fee (around £8.9 million) with his current employers, Paris Saint-Germain.
The newspaper adds that a five-year deal awaits the United States international forward, who the son of Liberian legend, George.
Lille could face Celtic in next season's Champions League, having finished runners-up behind PSG.
Meanwhile, another of Rodgers' winter recruits, Jeremy Toljan, could join Borussia Monchengladbach from namesakes, Dortmund, Bild reports.
Was Weah under-used by Celtic?
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