The club have baulked at Napoli's £150m valuation of the Senegalese defender.
But they haven't wasted any time sourcing another target, according to the Daily Star.
22-year-old Dias is six years younger than Koulibaly and would only cost the club a fee of £52m, which is included in his current contract.
Benfica have been trying to increase that clause to £87m, but United are hopeful they can swoop in before the changes are made.
Dias already has nine caps for Portugal.