The report states that United have re-kindled interest in the 25-year-old midfielder and established contact with the players uncle and agent Ihsan Gündoğan.
The Germany international recently signed a contract extension with the Bundesliga side however, he has recently also been linked with a move to Juventus.
Juventus manager Massimiliano Allegri is keen on a move for Gundogan according to Calciomercato.
The Italian sports paper states that the experienced manager wants reinforcements following an injury to their new signing Sami Khedira.
The 25-year-old previously turned down a contract offer from Dortmund but changed his mind regarding his future following discussions with their newly appointed manager Thomas Tuchel.
Gündoğan wrapped up the season with five assists and three goals in 33 appearances in all competitions.