The Red Devils are on the lookout for an experienced striker who could add a physical presence and goals to the team midseason.
Mandzukic was a summer target, but the clubs could not agree on a fee late in the transfer window.
ESPNsays United want to sign the player, but they want to ensure the 33-year-old reduces his wage demands first.
Another report suggests United will offer Mandzukic £85,000-a-week, which is almost equivalent to his existing salary at the Italian club.
But the Croatian could be looking for a pay rise in what would be his final major contract as a footballer.