The Germany international is out of contract next summer and he has turned down Dortmund’s offer of an extension, fuelling rumours he could leave as early as this summer.
United and Barcelona have been linked with the 24-year-old, but his future could still be in Westphalia, according to the Bundesliga club’s general manager Hans-Joachim Watzke.
“Maybe there is still a chance that he has a rethink,” he told the WAZ newspaper. “We are in talks and Ilkay is a decent lad.”
Gundogan joined Dortmund from Nurnberg in 2011 and has made 117 appearances for the Westphalian side, scoring 12 goals.
Injury restricted him to 23 appearances last season and ruled him out of last summer’s World Cup.