The 20-year-old continues to shine for Lille and his performances have caught the eye of English Premier League trio Manchester United, Arsenal and Chelsea.
There is also interest from Spanish giants Real Madrid and it only seems to be a matter of time before the France Under-21 international moves on.
Lille will not stand in the player's way, so as long as the offers match their valuation, there is a good chance a deal will happen.
Soumare did not cost Lille a penny after he arrived on a free transfer from Paris Saint-Germain in 2017 but now they will be holding out for a fee in the region of £43million.
Lille are under no pressure to cash in right now - Soumare still has two-and-a-half years remaining on his current contract - so they can play hard ball over offers.
The Ligue 1 side showed they are no pushovers when collecting top dollar for Nicolas Pepe, who eventually joined Arsenal in the summer, and they will stand firm again.
Lille also face a battle to keep hold of striker Victor Osimhen and central defender Gabriel, who are both in demand.
However, it is likely to be the summer before all the major transfer business is done, which will give Lille enough time to bring in suitable replacements.