He has already scored three this season, including two in two in the Eredivisie. Gakpo made his debut for Holland last year and has two goals in seven caps for his country.
Meanwhile, Antony is also keen to join United following strong interest. United saw an offer of around £67m turned down last week for the Brazil international.
However, Ajax believe they will return with an improved bid. If Antony were to leave, Chelsea star Hakim Ziyech would be their top target as a replacement.
Ziyech has been told he can leave Chelsea at the right price. The Morocco star joined the Blues from Ajax in the summer of 2020.
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