With the Hoops failing to retain the Scottish Premiership title, many have tipped Edouard to put an end to his four-year association with the club at the end of the season.
The France Under-21 international has been heavily linked with a host of clubs in the Premier League recently, including Arsenal and Liverpool.
However, Leicester are the only side likely to make a move for the 23-year-old when the transfer window opens in the summer as the Foxes view him as an option to strengthen their frontline.
It was expected that Edouard would be in the middle of a transfer scrap between Premier League sides, but that is not on the cards.
The former Paris Saint-Germain man has attracted little concrete interest from England ahead of the summer transfer window and Leicester look to be the only keen party.
Edouard has scored 16 goals from 26 league appearances for Celtic so far this season and sides are claimed to feel a fee of around £20m is justified.
The Hoops are not keen to part ways with the centre-forward at the end of the season and would have no problems with clubs not being interested in him.
