The Frenchman looks set to leave the Gunners in the wake of their FA Cup Final victory, with his current contract due to come to an end.
City have long been linked with the right-back’s signature, with some rumours suggesting that the player himself has already told close friends that he will be at the Etihad Stadium next season.
But now United are ready to take on their cross-city foes in the race for the £100,000-per-week star.
Van Gaal is believed to be convinced that Sagna is the right man to help the 2012/13 Premier League champions move forward and sees him as a more reliable option than Rafael.
The Dutch coach has not been officially revealed as United’s new boss, but an announcement is expected in the coming days.
The former Bayern Munich, Barcelona and Ajax chief will see out his role as Holland’s manager for the World Cup before relocating to Old Trafford.