The Denmark international spent part of last season on-loan with Napoli and two years to run on his Cherries deal. However, he is available from Bournemouth this summer.
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FCM chief Kristian Bach Bak has confirmed interest in Billing.
Bach Bak told TV2: "Of course Billing is interesting, but I think there's too many clubs.
"We are in a market where it is the calibre we are going up to strengthen the team. So of course he is an interesting player."