Coman, who has not agreed on a new contract with Bayern, could be on the market this summer.
According to Sport1 journalist Florian Plettenberg, the winger's father, family friends and his agent Pini Zahavi are all pushing him towards a move to England.
Plettenberg tweeted: "Update [on] Coman: Bosses are sure that [Kingsley Coman] wants to extend.
"But they know that his father, Benoit Menye (family's friend) & Zahavi are forcing his move to [England].
"A boss from [Man Utd] told me: "We do not comment on rumors. We have scouts all over the world & Coman is very talented."
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