The South Korea international enjoyed a superb season in helping Napoli win the Serie A title but is now expected to leave the club this summer.
A release clause of around €50million that becomes active for a 15-day period from 1 July has alerted a number of clubs with United eager to bring him to Old Trafford.
Reports in Italy have suggested the 26-year-old has already agreed a move to Erik ten Hag’s side but were later dismissed by a member of his team.
Paris Saint-Germain are also among the sides eager to sign Kim but according to Sky Sport Germany, Bayern have made decisive steps in hijacking the move.
The German champions are now edging towards a verbal agreement with the centre-half with talks expected to pick up speed following South Korea’s international fixtures against Peru and El Salvador.
United remain interested in signing Kim but now face serious competition for his signature.
United’s summer transfer business, which has been complicated by the club’s ongoing takeover saga, has seen them target Chelsea midfielder Mason Mount.
An opening bid of £40million was rejected by the Blues this week with signing a new striker also a top priority.
The club have however ended their interest in signing Harry Kane this summer, viewing Tottenham’s £100m valuation for a player with just one year left on his contract as excessive.
United will face similar problems trying to sign Kim’s Napoli teammate Victor Osimhen who is valued at £130m.
Atalanta starlet Rasmus Hojlund is another option under consideration with United ready to make an opening bid for the 20-year-old.
The Dane fuelled talk of a move to Manchester into this week when he admitted he could be on the move this summer.
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