The Gunners have been tracking the classy 21-year-old for the best part of 12 months, coming close to securing a £30m deal for his signature earlier this year.
But now United are also in the battle, with scouts from Old Trafford understood to have been present at recent Schalke games to watch the playmaker in action.
Louis van Gaal is rumoured to have cash to spend once again in 2015, despite having splashed over £150m during the summer – the largest amount of any club in Europe.
Even with Angel di Maria, Juan Mata and Wayne Rooney in his squad, the Dutchman is thought to be a fan of Draxler, who is considered to be one of the best young players in his position in European football.
The 15-time Germany international has indicated in the past that his future may be away from Gelsenkirchen, with talk of a £30m valuation having been doing the rounds.
His team-mate Benedikt Howedes is also on LVG’ radar.