The pair, 19 and 20-years-old respectively, have been tracked by the Hammers for the past couple of weeks, and having already utilised the French market this summer, West Ham want to bring in more players.
They are both young prospects, and would unlikely be signed to move into the Hammers' first-team, but clearly Slaven Bilic and his scouting team have seen enough to want to bring the pair to the Boleyn ground.
Who are Jonathan Bamba and Dylan Saint-Louis?
Bamba and Saint-Louis are both wingers, able to play on both sides of the field, whilst the latter can also play up front.
Bamba has played four times for the Saint-Etienne first-team, and has two goals in four games for the French Under-18 team.
Saint-Louis has yet to play for the senior team, nor for France’s youth teams, but both are highly-rated in the Ligue 1 club’s set-up.
It is unlikely that the club will want to sell two of their highly rated assets, but if the Hammers can guarantee them a passage into first-team football in the Premier League, they may be tempted to transfer to England.