The Hammers are reportedly set to pay around £10.7m for the U20 French international player.
Moukoudi is a very powerfully-built centre-back, and he made his debut for Le Havre in 2016.
The 20-year-old's French compatriot Issa Diop also completed £22m move to West Ham in June, and Moukoudi seems set to join him.
The club have already spent more than £100m on new signings this window, bringing in eight new names.
Felipe Anderson and Andriy Yarmolenko were both brought in, as well as Ryan Fredericks and Jack Wilshere on free transfers.