The 27-year-old looks like taking in a spell away from the Liberty Stadium.
Dyer has been a key figure at the Liberty Stadium since arriving there from Southampton in 2009, being a regular goal contributor in their time in the Premier League.
He has made 271 appearances for the Swans, netting 31 times, but the 27-year-old has found playing time a little harder to come by this season after the signing of Andre Ayew and the sensational form of Jefferson Montero, and Sky Sports say he is set to switch to the King Power Stadium for the rest of the campaign.
Of Swansea's four Premier League games, Dyer has featured in just one, coming on for the last 18 minutes of the Welsh outfit's win over Newcastle United. He did start and score in the 3-0 win over York City, but those limited minutes are surely an indication of where he rests in the club's first team plans unless there are injuries.
Leicester, on the other hand, have been eager to recruit alternatives on the wing, despite the strong performances of Marc Albrighton and Riyad Mahrez.
The Foxes had been looking at other wide options aside from Dyer, with Peru international Andre Carrillo said to be in talks on deadline day, as well as interest in unsettled Stoke forward Jon Walters and Hull's Ahmed Elmohamady, says the Independent.