Shaw has missed the last three games with a hamstring injury and the boss has admitted he will not return in time for the trip to the London Stadium.
Ole also told reporters after Thursday's FC Astana match that Paul Pogba and Anthony Martial look set to miss the encounter through respective knocks.
When asked if he thought the French duo would be available for the clash with the Hammers, Ole replied:
“Not really, no. They have not been training yet.
“Luke won’t be ready,”he added.
The Norwegian also gave an update on winger Daniel James, who picked up an ankle problem in last week’s victory over Leicester City.