Swansea are in the market for a new manager after they sacked Michael Duff following a run of poor form.
The Welsh side are sitting 18th in the Championship standings and are without a win in five league games.
They are now looking for a new manager and Davies has been one of the top names on their wish list of managers.
The Tottenham coach was on Swansea’s shortlist in the summer as well before they decided to bring in Duff.
But it has been claimed that their approach for the 38-year-old has been rejected by the north London club.
Ange Postecoglou does not want to lose his trusted lieutenant, who has been playing a key role under him.
Davies is a highly-rated coach who also worked under Brendan Rodgers at Liverpool, Celtic and Leicester City.
He also worked at Swansea previously as a performance analyst and coached their reserve side.