The Metro went onto say that Gündoğan is already believed to have agreed personal terms with United.
Squawka has also stated that the 24-year-old will join United while Calcio Mercato claimed the Germany International will be making the switch to Old Trafford.
With both Bayern Munich and Barcelona seemingly out of the race to sign Gündoğan, the Red Devils have emerged as favourites to sign the deep-lying-playmaker.
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The 24-year-old rejected a contract extension deal with Dortmund and is expected to leave the Bundesliga outfit.
Dortmund CEO Hans Joachim Watzke has previously confirmed that Gündoğan will leave the club at the end of the season.
“Gündoğan will be leaving Borussia Dortmund this summer, that is a fact. I am very confident we will see various clubs coming in for him,” Watzke told SportBild.
Gündoğan has five assists and three goals in 32 appearances for Dortmund despite spending much of the season out injured and is almost certain to leave the Bundesliga giants over the summer.