Former Swans boss Paulo Sousa tabled the offer for the Wales international, 26, who is under contract at the Liberty Stadium until 2013.
Swansea chairman Huw Jenkins said: "We have received a bid from Leicester City for Ashley Williams and have turned it down. The player is not for sale."
The current Welsh Footballer of the Year is away with John Toshack's Wales squad as they prepare for Friday's opening Euro qualifier in Montenegro.
Source: PA
