The young Swede was expected to be recalled from his loan by parent club Bayern Munich.
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However, Sky Deutschland says it's now been decided he will remain with Fulham for the rest of the campaign.
Fulham management are satisfied with Kusi-Asare's recent progress in training.
Fulham boss Marco Silva is also said to be planning to give the Swede more playing time during the second half of the season.
In total, Kusi-Asare has earned just 28 minutes in competitive games during the first part of the loan.