Ben Yedder has been on the books of Toulouse since 2010 and has a contract until June 2017.
The former France Under-21 international striker is rated as one of the best players in Ligue 1 and has been linked with a number of clubs.
According to Il Corriere Dello Sport, Italian clubs AS Roma and Juventus, and Spanish outfit Sevilla are also monitoring the 25-year-old.
Ben Yedder has scored 16 goals and created 28 chances in 33 Ligue 1 appearances for Toulouse this season.
The striker has a pass accuracy of 73% and a shot accuracy of 60%, and has won 20 headers, 23 dribbles and 18 tackles.
The Frenchman would be a good signing for West Ham, who will have to reinforce their attack in the summer in order to compete for a top-four finish in the Premier League next season.