Asensio enjoyed a successful loan spell during the second half of last season and Emery would like to be reunited with the Spain international before the end of the current window.
Villa have been exploring the possibility of striking a deal with Paris Saint-Germain, who consider the 29-year-old surplus to requirements.
Asked on Friday about the possibility of bringing Asensio back, Emery replied: “The transfer window finishes for every team on September 1 at 7pm - I know the time as well! We have to be alert in case we can add players, to bring them and help us increase the level and capacity in the squad.
“We have to mix the rules of UEFA and the capacity and possibility we can have to bring in good players to add to the squad.”
Morgan Rogers has been declared fit for Saturday’s Premier League opener against Newcastle, after recovering from the ankle injury he sustained in a pre-season friendly against Roma.
Midfielder Jacob Ramsey is on the verge of joining the Magpies in a deal worth a guaranteed £39m but the move will not be registered in time for him to face his former club.