The Swansea City player spent last season on loan at Sunderland, but is now being targeted by Villa with reports claiming a £6million deal was close.
However, Ki’s agents have told the local Korean media there has been no contact from Villa for their client's services.
"We have not heard from Aston Villa about signing Ki. He will return to Swansea (after his break in Korea)," a spokesperson for Global Sports Agent C2 said.
However, Villa sources have told Sky Sports that they are interested in securing a deal.
Ki joined the Swans in the summer of 2012 from Scottish side Celtic but was loaned out to Sunderland the following season despite being a regular in the team, and he impressed hugely on Wearside under Gus Poyet.
He also featured in every minute of South Korea’s World Cup campaign in Brazil and Swansea insist he could yet have a future at the Liberty Stadium and they would like him to sign a new deal.
"We want him to come back after his break and sit down with Garry (Monk) for a chat," Swansea chairman Huw Jenkins told the Evening Post.
"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."