The Sunday Express says United believe they can land Germany World Cup defender Hummels for around £25m.
Discussions with Dortmund have also included a firm enquiry for German international midfielder Marco Reus.
Sources close to Reus say he regrets turning down United earlier this year as he expected Barcelona to come good with an offer to BVB. Reus is furious being left hanging by the Catalans and is anxious for Van Gaal to revive United's proposal.
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