The German centre-back – who starred for his home nation as they lifted the World Cup over the summer – has been in impressive form for Schalke for some time, attracting attention from a number of Europe’s big hitters.
United have been heavily linked with the 26-year-old, but Arsenal look set to push ahead of their rivals after scouting him during last week’s 4-0 win over Stuttgart.
Wenger is believed to be concerned by a lack of depth at the back, which was once again exposed yesterday as full-back Mathieu Debuchy played at the centre of the backline due to a series of injuries.
Schalke are thought to be open to a deal, but only if an interested part pays around £15m.
Howedes is most comfortable at centre-back, but he starred for Germany in Brazil as a left-back.
United may mount a rival move, but international team-mates such as Mesut Ozil, Lukas Podolski and Per Mertesacker at Arsenal may boost the Gunners’ hopes.