The Premier League trio have all been chasing the Germany international for much of the summer, with the player himself expected to leave BVB in the not too distant future.
Reus recently rejected a new contract at the Westfalenstadion, leaving the release clause in his deal, which will drop to just below £20m next year, in place.
Real Madrid are rumoured to be working on a cut-price move for January which will include the money Dortmund owe them for Nuri Sahin being cancelled out, but Liverpool, Arsenal and United are also in the battle.
Reports suggest that the latter were rejected by the 25-year-old not long ago, but Louis van Gaal’s side may be able to persuade him to relocate to Old Trafford if they return to the Champions League.
Liverpool and Arsenal are both interested as well, with the Londoners having discussed a deal with his representatives.
Bayern Munich are hovering in the background, but Dortmund are reluctant to do business with their bitter rivals again.
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