The Trinidad and Tobago international has emerged as a key player for the Swans and has scored 45 league goals in 82 starts since arriving from St Johnstone two years ago.
Former Liberty Stadium boss Roberto Martinez is considering an attempt to take Scotland with him to the Latics and has held initial informal talks.
Burnley have also been in touch with Swansea chairman Huw Jenkins, although manager Owen Coyle was keen to stress that no bid has been tabled, despite Swansea's claims last week.
"At no time have we made a written offer for Jason Scotland," he told the Lancashire Evening Telegraph.
"There was a private conversation between Brendan Flood (Clarets operational director) and Huw Jenkins where they spoke about the player.
"I've always said that we are discreet and will always keep our business close to our chest."
Jenkins revealed that there had been further contact from the Latics, but again no official offer has been made.
He told the South Wales Evening Post: "I have had a chat with Wigan about Jason Scotland.
"They have not made an offer, but they have asked to be kept informed of Jason's situation."