The Argentina international's future has been the subject of much speculation in recent weeks, with Villa one of a number of clubs believed to be interested in his services.
Despite the transfer talk, the 31-year-old has started the 2023-24 campaign in Sevilla's first XI, playing the full 90 minutes against Valencia in La Liga last week, in addition to the whole game against Manchester City in the UEFA Super Cup on Wednesday night.
According to TyC Sports, Acuna has now come to an agreement with Villa over personal terms, although the two clubs are yet to settle on a transfer fee for the defender.
The report claims that Sevilla would be looking for around £13m for the South American, and it is unclear at this stage whether Villa would be prepared to pay that fee.
Acuna made the move to Estadio Ramon from Sporting Lisbon in 2020, and he has represented his Spanish side on 125 occasions in all competitions, scoring five goals and registering 13 assists in the process.
Meanwhile, according to Football Insider, Fulham are still concerned when it comes to the future of Willian.
The Brazilian left Craven Cottage on a free transfer last month before re-signing for Marco Silva's side, with his current deal due to run until the end of next season.
However, there remains speculation surrounding the 35-year-old's future, with Saudi Arabian side Al Shabab believed to be making a strong attempt to sign him.
Fulham are believed to be worried that Willian could leave before the end of the transfer window, with various reports claiming that he has already agreed personal terms with Al Shabab.
The Brazilian played the opening 45 minutes of Fulham's 1-0 win over Everton in the Premier League on Saturday.
In total, the former Chelsea forward has represented Silva's side on 31 occasions, scoring five goals and providing six assists, since making the move from Corinthians on a free transfer.
Staying with the Saudi Pro League, Al Fateh are reportedly bidding to sign AC Milan forward Divock Origi before the end of the transfer window.
The Belgium international is not in the plans of Milan head coach Stefano Pioli moving forward and will be allowed to leave the Italian giants in search of pastures new.
According to Football Insider, Al Fateh, who are managed by Slaven Bilic, are determined to bring the experienced forward to Saudi Arabia.
The 28-year-old started his professional career at Lille before moving to Liverpool, and he managed 41 goals in 175 appearances for the Premier League giants before leaving for Milan.
Origi found it difficult to make his mark for the San Siro outfit last term, though, only scoring twice in 36 appearances in all competitions.
Al Fateh, who finished sixth in the Saudi Pro League last season, also have the likes of Jason Denayer and Cristian Tello on their books.