Dembele who has been linked with a move to Chelsea in the January transfer window was pictured on a flight to London intensifying rumours that he is on his way to sign for Chelsea.
It has however been revealed that the French youngster was on his way to see Andy Williams, a knee specialist used by Celtic and based in London.
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The Premier League leaders want Dembele as an understudy to Diego Costa as Michy Batshuayi is a loan target for West Ham.
Celtic are however insisting that the 20-year-old is not for sale at the moment.
Since joining the Scottish giants in 2016, Dembele has become one of the hottest prospects in Europe.
If he eventually stays at Celtic this January, a move to a top European team is expected in the summer.