Everton, Leicester City and Leeds United all had scouts watch the Frenchman against Dundee United on Saturday, and the trio of Aston Villa, Crystal Palace and Newcastle United are also keen.
Edouard has been linked with a Celtic exit after the Scottish Premiership giants crashed out of the Champions League qualifying campaign on Wednesday night, missing out on the group stages for the third campaign in a row, and a move to the Premier League could be on the cards.
Leeds are set to announce the arrival of Spain international striker Rodrigo from Valencia, and that could see them pull out of the race for the France youth international.
Everton could launch a firm bid for Edouard after he scored 21 goals in 27 Scottish Premiership games last term, but they will have to offer around £30 million to have a chance of landing him.
The 22-year-old wants to play Champions League football, and Leeds and the Toffees aren’t able to offer that at the moment.
Leicester came close to a top-four finish last term and will look to go one better next season.
Foxes manager Brendan Rodgers signed Edouard for Celtic and is keen on a reunion as he seeks a long-term replacement for Jamie Vardy.