The report states that United are close to completing the transfer and have already started planning ahead to signing their other summer targets.
Girlfriend of Gündoğan, Sila Şahin whipped up a social media storm when she shared an Instagram picture of a flight board displaying the city of Manchester earlier this week.
Manchester United have been closely linked with Gündoğan ever since he rejected extending his contract with Dortmund.
“Playing outside Germany is one of my big goals. If one day I leave here, I’d like to play in Spain or for one of the big teams in England,” Gündoğan was quoted as saying in the Daily Mirror at the turn of the year.
Gündoğan has four assists and three goals in 31 appearances for Dortmund despite spending much of the season out injured.