Red Devils boss Erik ten Hag is an admirer of the well-travelled forward, who has played his club football in the Netherlands, Italy, Germany, England and China.
Manchester United are keen on the 33-year-old attacker as Ten Hag looks to strengthen his squad depth at Old Trafford.
And Arnautovic, who is currently on the books at Italian side Bologna, wants to move on before the transfer window closes.
The Serie A outfit have rejected one offer from Manchester United in recent days and do not want to lose Arnautovic.
However, with the Austrian keen to move on, Bologna could be forced to rethink their stance.
Bologna signed Arnautovic following a spell in Chinese football for the forward, who joined Shanghai Port in 2019 from West Ham.
Manchester United have until 1st September to do a deal with Bologna to add Arnautovic to Ten Hag’s squad.
