The 36-year-old is believed to be keen on a return to England after enjoying two seasons at Tottenham between 2005-07.
Portsmouth are also reported to be weighing up a move for the midfield dynamo, but Leicester are hoping to lure the Dutchman to the Walkers Stadium.
Leicester manager Nigel Pearson said: "When players become available, if they are the right players for us then we investigate it. There has been interest but after that I am not in a position to comment further. There is nothing to elaborate on at the moment.
"There has been interest in both directions, but whether it comes to anything is another story."
Davids has enjoyed a glittering career after coming to the fore at
Ajax in the early 1990s.
He has played for the likes of AC Milan, Juventus, Inter Milan and Barcelona before pitching up at Spurs and if Leicester can convince him to return to England he could be plying his trade in the Championship.