The Argentina international's future has been the subject of much speculation over the last week, with Villa seemingly determined to bring him to Villa Park before the end of the transfer window.
According to Football Insider, discussions between the two clubs continued on Saturday, and it is understood that the left-back has already come to an agreement with Unai Emery's side over personal terms.
Villa are therefore attempting to negotiate a transfer fee with Sevilla, who are believed to be open to letting him leave for the right price this summer.
The 31-year-old has been with his current side since 2020, featuring on 125 occasions in all competitions.
Acuna, who played the full 90 minutes against Manchester City in the UEFA Super Cup on Wednesday, has another two years left to run on his contract at Estadio Ramon.
Elsewhere, Sunderland have reportedly informed Burnley that it will cost £15m to sign English attacker Jack Clarke before the end of the transfer window.
Vincent Kompany's side are believed to have submitted a £10m offer for Clarke, with the deal potentially rising to £12m in add-ons, but Sunderland turned it down.
According to Football Insider, the Black Cats have told Burnley that Clarke will cost £15m, and it is believed that the Clarets would be prepared to go to that price to secure his signature.
Sunderland are in a strong position when it comes to the 22-year-old's future, as his contract at the Stadium of Light has another three years left to run.
Clarke has scored once in four appearances for the Black Cats this season, finding the back of the net against Preston North End on August 12.
The attacker was also in excellent form for Sunderland during the 2022-23 campaign, scoring 11 goals and registering 14 assists in 50 appearances in all competitions.
Meanwhile, according to transfer expert Fabrizio Romano, a number of Qatari clubs are competing to sign Philippe Coutinho before the end of the summer transfer window.
The 31-year-old only managed one goal in 20 Premier League appearances for Aston Villa during the 2022-23 campaign, and he is widely expected to leave the club before the end of the transfer window.
Romano claims that Qatari clubs are pushing to sign the Brazilian, while there is also said to be interest from Saudi Arabia in the experienced playmaker.
Coutinho, who has a contract at Villa Park until June 2026, was involved in his side's opening match of the new Premier League season, featuring as a late substitute against Newcastle United.
Once regarded as one of the best attacking midfielders in world football, the South American has seen his career stall in recent years, struggling at Barcelona before leaving to return to the Premier League.
Villa have lost Emiliano Buendia to a long-term knee injury, but the club have boosted their attacking options with the recent addition of Nicolo Zaniolo on loan from Galatasaray.