Villa have been linked with a move for the South Korean playmaker, but it is the Black Cats who hold the advantage over their Premier League rivals, despite reports that manager Paul Lambert is close to signing the midfielder.
Ki spent last season on loan with Sunderland and enjoyed a good campaign at the Stadium of Light, and manager Gus Poyet is keen to secure him on a long-term deal, according to The Chronicle.
The Uruguayan coach is said to view Ki as an ideal player to fit into his passing game, and it is believed that Poyet wants him to sign permanently, despite not having tabled a formal offer at this stage.
Lambert is also a keen admirer of Ki, although the Scot is having to juggle his transfer dealings on a virtual shoe-string budget after owner Randy Lerner's decision to try to sell the club after the end of last season.
The former Norwich City boss has so far added Philippe Senderos, Joe Cole and Kieran Richardson to his side, but he is unable to compete financially with most of the division, after their American owner put the club on the market.
Swansea City chairman Huw Jenkins made no secret of his desire to try to keep Ki at the Liberty Stadium next season.
He said: “We want him to come back after his break and sit down with Garry [Monk, the Swansea manager] for a chat. Garry has spoken to him already, but it’s important that they have another chat and we will decide on where we go after that. Ideally, we would like to tie Ki up on a long-term contract. There’s no hiding from that.”
Despite the Welshman's public declarations and Villa's interest, Ki's time with Sunderland last year could be crucial, and the 25-year-old could make the switch to the North East on a permanent deal, if the Black Cats step up to the plate with a formal offer.