The Red Devils have made the Bundesliga playmaker one of their top targets heading towards the summer, with David Moyes desperate to rebuild his midfield after a difficult season.
The Scot has struggled to echo the form of predecessor Sir Alex Ferguson, with disappointing form of his central players seen as a major contributing factor.
Gundogan has been hailed as the man to solve Moyes’ problems, with the German international having been lauded for his range of passing and physicality.
A swoop has long been considered as a difficult one, but United have been buoyed by news that Dortmund are keen on Kagawa.
The Japanese passer moved to Old Trafford from the Westfalenstadion in 2012 for £16m, but has failed to make a real impact.
Dortmund are considering taking him back, which has opened the door to him being used as a sweetener in a deal for Gundogan.
United also want Marco Reus, but the winger – who is one of last season’s Champions League runners-ups’ first-team stars – is believe to be unavailable.