The Villa Park club are interested in strengthening their back line, as they will likely lose the 21-year-old and other loan signings from last season.
One name that is interesting Dean Smith's men is 23-year-old Targett, per The Sun.
Targett is not a regular at Southampton, which could tempt him to move to a newly promoted side.
The left-back is behind Ryan Bertrand in the Saints pecking order under Ralph Hasenhuttl.
He does have a contract until 2022, which means he will not come cheap for Villa.