He is on the look out for a new club after turning down a contract at Pride Park last summer.
Kinkladze will train with the Leeds squad with a view to securing a move back into The Premiership at Elland Road.
With the player being available on a free transfer he would fit the bill for Leeds as they have no money available to buy any new players.
The 30-year-old was close to a move to Panathinaikos last month, but the Greek outfit failed to offer him a deal after a short trial spell at the club.
The Georgian international is best remembered by his time in England with Manchester City, when he earned the reputation as one of the most skilful players in the country.