The striker has been heavily linked with a move away from Celtic before the transfer window shuts on 5th October and he is not short of admirers.
Celtic slipping out of the Champions League qualifiers also increased speculation around his future, but playing in the Europa League and helping the Bhoys win a tenth title in a row are factors pushing Edouard to stay.
It is claimed that Edouard does want a new challenge soon, but is happy with life at Celtic at present.
The French striker, who is keen to be playing regular Champions League football to push for a spot in the senior France squad, is likely set to be content with Celtic either selling him or keeping him in the ongoing window.
Celtic would need to be made an offer they cannot refuse to let Edouard go before the window closes.
Both defender Kristoffer Ajer and midfielder Oliver Ntcham are rated as more likely departures than Edouard.
The hitman was an unused substitute on Saturday when Celtic beat Livingston 3-2 in the Scottish Premiership.