Gundogan will be available for around £20m this summer as he only has one year remaining on his current deal.
Reports last week suggested Man United had already agreed a transfer with Dortmund for Gundogan but the club have since denied this.
Arsenal have now signalled their intention to challenge United for the player’s signature as they look to boost their midfield options.
The news will worry United fans but it appears that the club have already made contact with Gundogan over a potential move.
However, Arsenal are a massive club and would be an attractive destination for the 24-year-old.