A method performed in a data processing system initiates an asynchronous memory move (AMM) operation, whereby a processor performs a move of data in virtual address space from a first effective address to a second effective address and forwards parameters of the AMM operation to asynchronous memory mover logic for completion of the physical movement of data from a first memory location to a second memory location. The processor executes a second operation, which checks a status of the completion of the data move and returns a notification indicating the status. The notification indicates a status, which includes one of: data move in progress; data move totally done; data move partially done; data move cannot be performed; and occurrence of a translation look-aside buffer invalidate entry (TLBIE) operation. The processor initiates one or more actions in response to the notification received.