According to reports in England, Leicester City have won the race for his signature.
It would see the Frenchman link up once again with Brendan Rodgers.
The former Celtic manager views Edouard as the long-term replacement for Jamie Vardy.
The England international has 12 goals in 23 Premier League appearances and is contracted to 2023 by which point he will be 36.
Leicester are close to agreeing a fee of £15million, report the Daily Mail, with Edouard keen on the move.
The 23-year-old has a record of better than one goal every other game, scoring 21 in 34 since August.
A chunk of the reported £15million would go to former club Paris Saint-Germain due to a clause in the deal which brought him to Parkhead.
Edouard had previously been linked with moves upwards of £25million with Celtic likely to negotiate a large sell-on fee for themselves if he moves on from Leicester.