The Georgian playmaker has been training with The Whites and has figured for the club's second string.
The former Derby County and Manchester City man was hoping to earn a deal with Leeds and a return to The Premiership, but it now looks as though that quest has ended.
Kinkladze rejected the offer of a new deal with The Rams last summer and left Pride Park in search of another club.
After being linked with moves to Dundee and MLS side Chicago, Kinkladze ended up at Elland Road.
Caretaker boss Eddie Gray had been taking a look at him but after he reportedly turned up late for training on a number of occasions, the club ended his trial.
The 30-year-old will now have to look around for another opportunity to breathe life into his flagging career.
