The newspaper claims Targett is Dean Smith's first choice candidate to come and add some competition in Villa's left-back position.
The Southampton academy product was also a target for Smith's predecessor as Aston Villa manager, Steve Bruce, according to The Mirror.
However, a proposed loan move failed to materialise during last summer's transfer window, while Targett later saw a January transfer to Fulham fall through, after a successful spell on loan there.
And Aston Villa may have better luck this time, after the 23-year-old ended last season as Southampton's second choice in his position.
But the Saints are likely to hold plenty of power should it come to negotiate, having tied him to a five-year contract in 2017.
Would the Southampton left-back be a good addition for Aston Villa?
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