The Daily Mail says Mandzukic plans to start training with United ahead of a potential January transfer.
According to reports in Italy, the forward will move to Manchester as soon as an informal agreement is reached between the two clubs, giving him time to settle in before the deal goes through.
The 33-year-old has been frozen out by Juve manager Maurizio Sarri, failing to make a single appearance for the first team this season.
United will have to spend £10million if they want to sign Mandzukic in the January transfer window.
United boss Ole Gunnar Solskjaer wants Croatian star Mandzukic to beef up his misfiring front line.