The 29-year-old, whose contract runs out in the summer, is widely expected to be leaving the Emirates Stadium this year.
Manchester City have long been interested in Sanchez, but Manchester United and Liverpool have also reportedly thrown their names in the hat for the Chilean's services.
According to The Guardian, the former Barcelona forward has not travelled to the south coast with the rest of the Gunners squad and is believed to favour a move to United over City.
The report goes on to claim that United have moved ahead of their cross-town rivals with a more lucrative package, while Arsenal harbour hopes of recruiting Red Devils midfielder Henrikh Mkhitaryan.
Sanchez has made 166 appearances for Arsenal, scoring 80 goals and registering 46 assists.