The 17-year-old centre-back has broken in the first team of Ligue 2 side Valenciennes this season and has started the last six league games for the club.
His performances in the second tier of French football have been attracting the prying eyes of bigger clubs, both in France and the rest of Europe.
Arsenal and Leicester are also claimed to be keeping tabs on the young defender with a view to taking him to England in the summer.
But the first concrete move for Doukoure has been made by Strasbourg as, according to French outlet Foot Mercato, the French club have directly approached the player.
It has been claimed that the Ligue 1 side are in contact with the young defender and are trying to convince him to consider a summer switch.
The teenager still has two years left on his contract with Valenciennes and seems to have cemented his place in the starting eleven this season.
Interest from the Premier League could potentially turn his head, but Strasbourg are likely to offer him the chance to play regular first-team football next season in Ligue 1.
Strasbourg have identified Doukoure as the replacement for Mohamed Simakan, who will join RB Leipzig in the summer.