The Argentine left Juventus for Villa last summer and spent the second-half of last season on-loan with Valencia.
Il Resto del Carlino says agents are now in talks with Bologna about a Serie A return for Barrenechea.
A loan deal is being discussed, but an agreement on his value will need to be reached: Aston Villa price him at €15m, while the Rossoblu are starting at €10m.
There's plenty of competition: Porto and Benfica are also interested in Barrenechea, but the lure of Serie A and his familiarity with the Italian league could make the difference.