The 20 year old is currently on loan at League One leaders Shrewsbury Town but his contract expires at the end of the season. The England Under 21 international is said to want assurances from manager Jose Mourinho about his prospects of first team football.
Henderson is reportedly not keen on going back to youth team football, and wants to play regularly at senior level. With David De Gea obstructing his route to the first team at United, the Sun report he is prepared to move elsewhere.
Gunners boss Arsene Wenger was keen on signing a young goalkeeper in the summer but missed out on his main target Jordan Pickford. Henderson could move to the Emirates once his contract expires but as he is below 23, Arsenal will have to pay United compensation.
The Gunners do have rivals for his signature however with Championship clubs, and Portuguese champions Benfica, all reportedly interested in signing the stopper.