FootMercato claims the Frenchman could link up with former Hoops player David Moyes at the London Stadium by the end of the month, although there is no mention of any fee or length of contract.
Ntcham has been linked with moves away from Celtic, most notably Porto, Marseille and Lyon but FootMercato claims the player is in "advanced negotiations" with the English Premier League club.
The former Manchester City youngster has scored five goals and laid on four more for his colleagues in 31 matches so far this term. He netted an injury time winner in Rome as Celtic defeated Lazio 2-1 in November.
Reports in France claim the Hammers are also in talks with Pape Cheikh Diop, who is currently on loan at Celta Vigo from Lyon.