Earnshaw, whose first request to leave was turned down earlier in the month, has become frustrated at a lack of first-team opportunities. But Robson is mindful of the fact that the in-form Kanu will be unavailable during January because of Africa Cup of Nations commitments with Nigeria along with Senegal's Diomansy Kamara.
Robson said: "I've made my position very clear on this matter. We received a transfer request from Earnie two weeks ago which I turned down. Earnie has submitted another transfer request in the past few days which I have also turned down. Earnie has just got to knuckle down and fight for his place."
Earnshaw was the Baggies' leading scorer last season with 14 goals but has made only four League starts during the current campaign.