The Blues see the Canadian as a potential replacement for Gabon striker Pierre-Emerick Aubameyang, although they will need to fork out a fee between £38-46m.
The Chelsea hierarchy do not see Aubameyang as a long-term option for the Blues hence the need to sign David who is much younger.
The Canadian forward has so far scored nine goals in 11 appearances for Lille this season and is joint top scorer with Neymar Jr. and also has 20 goals in 30 appearances for Canada.
However the Blues will have to compete with fellow Premier League team Arsenal who have also been linked with the Canadian.
