The midfielder was unable to thrash out a fresh contract with Chelsea, and has been one of the most attrative Bosman transfers on the domestic market this close season.
Agent Jonathan Barnett told planetfootball that everything was close to being resolved between Peter Reid's Elland Road outfit, and the 24-year-old.
It is believed that the Hammersmith-born ace is to undergo a medical in Yorkshire on Thursday.
Morris had looked destined to join Cardiff City, but disappointed Lennie Lawrence by instead looking to secure a deal to remain in The Premiership.
"Terms have near enough been agreed," confirmed Barnett to planetfootball.com.
When asked if this was the reason the player rejected a move to Cardiff City, he replied: "It would seem so."
Reid has been desperate to bring in a new face to appease the Leeds faithful, and Morris, who was also strongly linked to Portsmouth, should fit the bill.
