David Moyes believes the Borussia Dortmund playmaker is the most likely of his midfield targets to move to Old Trafford this summer.
And United are confident they have got their man.
Any deal, though, would be dependent on Gundogan, 23, proving he has recovered from the back injury which has wrecked this season for him.
Any deal, however, hinges on the player proving his fitness after a back injury suffered in August that has ruined his season so far.
United's executive vice chairman, Ed Woodward, is said to have been working hard over the last few months on several sets of negotiations, which have also included Wayne Rooney's recently signed contract extension. Now, Woodward and Moyes allegedly have reason to believe that they have done enough to convince Gundogan that his future lies at United.
The Old Trafford club were given a potential green light on the deal earlier in February when Gundogan's father, who also serves as the player's agent, said the 23-year-old's future is "completely open". Gundogan will soon be entering the final year of his Dortmund contract and Die Schwarzgelben are believed to be willing to sell as they not keen to lose another of their star assets on a free transfer.
Since signing for Dortmund from FC Nürnberg in 2011, Gundogan has become one of Europe's finest young midfield talents. In 2012, the player helped his team to a league and cup double, while in 2013 he was a vital component of the side that wowed audiences en-route to the Champions League final at Wembley. An assured passer with great technical ability, Gundogan would add great quality to the ailing centre of United's midfield.
It is possible that Shinji Kagawa, who joined United from Dortmund, could return to his former club in a swap deal.
Moyes is also a big fan of Bayern Munich midfielder Toni Kroos.
But Kroos, 24, is expected to sign a new deal with European champions.